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Show that *: R × R ⊠⊠ R given by a * b ⊠⊠ a + 2b is not associative.

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The operation * is not associative, since

(8 * 5) * 3 = (8 + 10) * 3 = (8 + 10) + 6 = 24, while 8 * (5 * 3) = 8 * (5 + 6) = 8 * 11 = 8 + 22 = 30.

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Show that *: R × R ⊠⊠ R given by a * b ⊠⊠ a + 2b is not associative.

Verified Answer

Show that : R × R ⊠⊠ R given by a b ⊠⊠ a + 2b is not associative.