diff --git a/jest.config.js b/jest.config.js
index 1d4488d6904d..c6661b005dea 100644
--- a/jest.config.js
+++ b/jest.config.js
@@ -31,6 +31,7 @@ module.exports = {
   ],
   testEnvironment: './packages/jest-environment-node',
   testPathIgnorePatterns: [
+    '/__arbitraries__/',
     '/node_modules/',
     '/examples/',
     '/e2e/.*/__tests__',
diff --git a/package.json b/package.json
index 504eeb41d7e3..ae5ee0e2378b 100644
--- a/package.json
+++ b/package.json
@@ -39,6 +39,7 @@
     "eslint-plugin-react": "^7.1.0",
     "eslint-plugin-relay": "~0.0.19",
     "execa": "^1.0.0",
+    "fast-check": "^1.12.0",
     "glob": "^7.1.1",
     "graceful-fs": "^4.1.15",
     "isbinaryfile": "^4.0.0",
diff --git a/packages/expect/src/__tests__/__arbitraries__/sharedSettings.ts b/packages/expect/src/__tests__/__arbitraries__/sharedSettings.ts
new file mode 100644
index 000000000000..98a48910811e
--- /dev/null
+++ b/packages/expect/src/__tests__/__arbitraries__/sharedSettings.ts
@@ -0,0 +1,22 @@
+/**
+ * Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved.
+ *
+ * This source code is licensed under the MIT license found in the
+ * LICENSE file in the root directory of this source tree.
+ *
+ */
+
+import fc from 'fast-check';
+
+// settings for anything arbitrary
+export const anythingSettings = {
+  key: fc.oneof(fc.string(), fc.constantFrom('k1', 'k2', 'k3')),
+  withBoxedValues: true,
+  // Issue #7975 have to be fixed before enabling the generation of Map
+  withMap: false,
+  // Issue #7975 have to be fixed before enabling the generation of Set
+  withSet: false,
+};
+
+// assertion settings
+export const assertSettings = {}; // eg.: {numRuns: 10000}
diff --git a/packages/expect/src/__tests__/matchers-toContain.property.test.ts b/packages/expect/src/__tests__/matchers-toContain.property.test.ts
new file mode 100644
index 000000000000..29e9b4c1d4e5
--- /dev/null
+++ b/packages/expect/src/__tests__/matchers-toContain.property.test.ts
@@ -0,0 +1,48 @@
+/**
+ * Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved.
+ *
+ * This source code is licensed under the MIT license found in the
+ * LICENSE file in the root directory of this source tree.
+ *
+ */
+
+import fc from 'fast-check';
+import {
+  anythingSettings,
+  assertSettings,
+} from './__arbitraries__/sharedSettings';
+
+describe('toContain', () => {
+  it('should always find the value when inside the array', () => {
+    fc.assert(
+      fc.property(
+        fc.array(fc.anything(anythingSettings)),
+        fc.array(fc.anything(anythingSettings)),
+        fc.anything(anythingSettings).filter(v => !Number.isNaN(v)),
+        (startValues, endValues, v) => {
+          // Given: startValues, endValues arrays and v value (not NaN)
+          expect([...startValues, v, ...endValues]).toContain(v);
+        },
+      ),
+      assertSettings,
+    );
+  });
+
+  it('should not find the value if it has been cloned into the array', () => {
+    fc.assert(
+      fc.property(
+        fc.array(fc.anything(anythingSettings)),
+        fc.array(fc.anything(anythingSettings)),
+        fc.dedup(fc.anything(anythingSettings), 2),
+        (startValues, endValues, [a, b]) => {
+          // Given: startValues, endValues arrays
+          //        and [a, b] equal, but not the same values
+          //        with `typeof a === 'object && a !== null`
+          fc.pre(typeof a === 'object' && a !== null);
+          expect([...startValues, a, ...endValues]).not.toContain(b);
+        },
+      ),
+      assertSettings,
+    );
+  });
+});
diff --git a/packages/expect/src/__tests__/matchers-toContainEqual.property.test.ts b/packages/expect/src/__tests__/matchers-toContainEqual.property.test.ts
new file mode 100644
index 000000000000..ab6145a645f7
--- /dev/null
+++ b/packages/expect/src/__tests__/matchers-toContainEqual.property.test.ts
@@ -0,0 +1,46 @@
+/**
+ * Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved.
+ *
+ * This source code is licensed under the MIT license found in the
+ * LICENSE file in the root directory of this source tree.
+ *
+ */
+
+import fc from 'fast-check';
+import {
+  anythingSettings,
+  assertSettings,
+} from './__arbitraries__/sharedSettings';
+
+describe('toContainEqual', () => {
+  it('should always find the value when inside the array', () => {
+    fc.assert(
+      fc.property(
+        fc.array(fc.anything(anythingSettings)),
+        fc.array(fc.anything(anythingSettings)),
+        fc.anything(anythingSettings),
+        (startValues, endValues, v) => {
+          // Given: startValues, endValues arrays and v any value
+          expect([...startValues, v, ...endValues]).toContainEqual(v);
+        },
+      ),
+      assertSettings,
+    );
+  });
+
+  it('should always find the value when cloned inside the array', () => {
+    fc.assert(
+      fc.property(
+        fc.array(fc.anything(anythingSettings)),
+        fc.array(fc.anything(anythingSettings)),
+        fc.dedup(fc.anything(anythingSettings), 2),
+        (startValues, endValues, [a, b]) => {
+          // Given: startValues, endValues arrays
+          //        and [a, b] identical values
+          expect([...startValues, a, ...endValues]).toContainEqual(b);
+        },
+      ),
+      assertSettings,
+    );
+  });
+});
diff --git a/packages/expect/src/__tests__/matchers-toEqual.property.test.ts b/packages/expect/src/__tests__/matchers-toEqual.property.test.ts
new file mode 100644
index 000000000000..ca7d88ef7390
--- /dev/null
+++ b/packages/expect/src/__tests__/matchers-toEqual.property.test.ts
@@ -0,0 +1,58 @@
+/**
+ * Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved.
+ *
+ * This source code is licensed under the MIT license found in the
+ * LICENSE file in the root directory of this source tree.
+ *
+ */
+
+import fc from 'fast-check';
+import {
+  anythingSettings,
+  assertSettings,
+} from './__arbitraries__/sharedSettings';
+
+describe('toEqual', () => {
+  it('should be reflexive', () => {
+    fc.assert(
+      fc.property(fc.dedup(fc.anything(anythingSettings), 2), ([a, b]) => {
+        // Given: a and b identical values
+        expect(a).toEqual(b);
+      }),
+      assertSettings,
+    );
+  });
+
+  it('should be symmetric', () => {
+    const safeExpectEqual = (a, b) => {
+      try {
+        expect(a).toEqual(b);
+        return true;
+      } catch (err) {
+        return false;
+      }
+    };
+    fc.assert(
+      fc.property(
+        fc.anything(anythingSettings),
+        fc.anything(anythingSettings),
+        (a, b) => {
+          // Given:  a and b values
+          // Assert: We expect `expect(a).toEqual(b)`
+          //         to be equivalent to `expect(b).toEqual(a)`
+          expect(safeExpectEqual(a, b)).toBe(safeExpectEqual(b, a));
+        },
+      ),
+      {
+        ...assertSettings,
+        examples: [
+          [0, 5e-324], // Issue #7941
+          // [
+          //   new Set([false, true]),
+          //   new Set([new Boolean(true), new Boolean(true)]),
+          // ], // Issue #7975
+        ],
+      },
+    );
+  });
+});
diff --git a/packages/expect/src/__tests__/matchers-toStrictEqual.property.test.ts b/packages/expect/src/__tests__/matchers-toStrictEqual.property.test.ts
new file mode 100644
index 000000000000..70dcd4e5cd1b
--- /dev/null
+++ b/packages/expect/src/__tests__/matchers-toStrictEqual.property.test.ts
@@ -0,0 +1,49 @@
+/**
+ * Copyright (c) Facebook, Inc. and its affiliates. All Rights Reserved.
+ *
+ * This source code is licensed under the MIT license found in the
+ * LICENSE file in the root directory of this source tree.
+ *
+ */
+
+import fc from 'fast-check';
+import {
+  anythingSettings,
+  assertSettings,
+} from './__arbitraries__/sharedSettings';
+
+describe('toStrictEqual', () => {
+  it('should be reflexive', () => {
+    fc.assert(
+      fc.property(fc.dedup(fc.anything(anythingSettings), 2), ([a, b]) => {
+        // Given: a and b identical values
+        expect(a).toStrictEqual(b);
+      }),
+      assertSettings,
+    );
+  });
+
+  it('should be symmetric', () => {
+    const safeExpectStrictEqual = (a, b) => {
+      try {
+        expect(a).toStrictEqual(b);
+        return true;
+      } catch (err) {
+        return false;
+      }
+    };
+    fc.assert(
+      fc.property(
+        fc.anything(anythingSettings),
+        fc.anything(anythingSettings),
+        (a, b) => {
+          // Given:  a and b values
+          // Assert: We expect `expect(a).toStrictEqual(b)`
+          //         to be equivalent to `expect(b).toStrictEqual(a)`
+          expect(safeExpectStrictEqual(a, b)).toBe(safeExpectStrictEqual(b, a));
+        },
+      ),
+      assertSettings,
+    );
+  });
+});
diff --git a/yarn.lock b/yarn.lock
index 22e5b83b0035..7d32f60984e1 100644
--- a/yarn.lock
+++ b/yarn.lock
@@ -5641,6 +5641,14 @@ fancy-log@^1.3.2:
     parse-node-version "^1.0.0"
     time-stamp "^1.0.0"
 
+fast-check@^1.12.0:
+  version "1.12.0"
+  resolved "https://registry.yarnpkg.com/fast-check/-/fast-check-1.12.0.tgz#bff7908aa357703f207ee1877ffcf4486a698aa0"
+  integrity sha512-r/zmvxG/8IsxyOzf9T6wnjJQjSLmymAETeRVfs4/0VzxBmyK48o871BRKmEIgEBLmrg9klh3e4A4BZc3yrH2QQ==
+  dependencies:
+    lorem-ipsum "~1.0.6"
+    pure-rand "^1.6.2"
+
 fast-deep-equal@^2.0.1:
   version "2.0.1"
   resolved "https://registry.yarnpkg.com/fast-deep-equal/-/fast-deep-equal-2.0.1.tgz#7b05218ddf9667bf7f370bf7fdb2cb15fdd0aa49"
@@ -8348,6 +8356,13 @@ loose-envify@^1.0.0, loose-envify@^1.1.0, loose-envify@^1.3.1, loose-envify@^1.4
   dependencies:
     js-tokens "^3.0.0 || ^4.0.0"
 
+lorem-ipsum@~1.0.6:
+  version "1.0.6"
+  resolved "https://registry.yarnpkg.com/lorem-ipsum/-/lorem-ipsum-1.0.6.tgz#69e9ab02bbb0991915d71b5559fe016d526f013f"
+  integrity sha512-Rx4XH8X4KSDCKAVvWGYlhAfNqdUP5ZdT4rRyf0jjrvWgtViZimDIlopWNfn/y3lGM5K4uuiAoY28TaD+7YKFrQ==
+  dependencies:
+    minimist "~1.2.0"
+
 loud-rejection@^1.0.0:
   version "1.6.0"
   resolved "https://registry.yarnpkg.com/loud-rejection/-/loud-rejection-1.6.0.tgz#5b46f80147edee578870f086d04821cf998e551f"
@@ -8912,7 +8927,7 @@ minimist@0.0.8:
   resolved "https://registry.yarnpkg.com/minimist/-/minimist-0.0.8.tgz#857fcabfc3397d2625b8228262e86aa7a011b05d"
   integrity sha1-hX/Kv8M5fSYluCKCYuhqp6ARsF0=
 
-minimist@1.2.0, minimist@^1.1.1, minimist@^1.1.3, minimist@^1.2.0:
+minimist@1.2.0, minimist@^1.1.1, minimist@^1.1.3, minimist@^1.2.0, minimist@~1.2.0:
   version "1.2.0"
   resolved "https://registry.yarnpkg.com/minimist/-/minimist-1.2.0.tgz#a35008b20f41383eec1fb914f4cd5df79a264284"
   integrity sha1-o1AIsg9BOD7sH7kU9M1d95omQoQ=
@@ -10690,6 +10705,11 @@ punycode@^2.1.0, punycode@^2.1.1:
   resolved "https://registry.yarnpkg.com/punycode/-/punycode-2.1.1.tgz#b58b010ac40c22c5657616c8d2c2c02c7bf479ec"
   integrity sha512-XRsRjdf+j5ml+y/6GKHPZbrF/8p2Yga0JPtdqTIY2Xe5ohJPD9saDJJLPvp9+NSBprVvevdXZybnj2cv8OEd0A==
 
+pure-rand@^1.6.2:
+  version "1.6.2"
+  resolved "https://registry.yarnpkg.com/pure-rand/-/pure-rand-1.6.2.tgz#90b3ae78efe36f7e6e27bfffedf934f77382e6e6"
+  integrity sha512-HNwHOH63m7kCxe0kWEe5jSLwJiL2N83RUUN8POniFuZS+OsbFcMWlvXgxIU2nwKy2zYG2bQan40WBNK4biYPRg==
+
 q@0.9.7:
   version "0.9.7"
   resolved "https://registry.yarnpkg.com/q/-/q-0.9.7.tgz#4de2e6cb3b29088c9e4cbc03bf9d42fb96ce2f75"