) ∉ 0 . Other properties need not be checked as it is not
Chapter 9: Chapter 12 · MATHEMATICS-VOLUME 2 · EN medium
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) ∉ . Other properties need not be checked as it is not a binary operation. Example . Verify (i) closure property (ii) commutative property, and (iii) associative property of the following operation on the given set. a b a b ∗ ∀ ; (exponentiation property) (i) It is true that a b a b ∗ ∀ ; . So ∗ is a binary operation on . (ii) a b a b ∗ and b a b a ∗ . Put, a = and b = . Then a b ∗ but b a ∗ So a b ∗ need not be equal to b a ∗ . Hence ∗ does not have commutative property . (iii) Next consider a b c b c ∗ ∗ ∗ ) . Take a and c = . Then a b c ∗ ∗ ∗ ∗ But a b bc bc ∗
📖 Class 12 Mathematics English Volume 2 2025 Edition www.tntextbooks.in · Page 234
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) ∉ . Other properties need not be checked as it is not a binary operation. Example . Verify (i) closure property (ii) commutative property, and (iii) associative property of the following operation on the given set.
a b a b ∗ ∀ ; (exponentiation property) (i) It is true that a b a b ∗ ∀ ; . So ∗ is a binary operation on . (ii) a b a b ∗ and b a b a ∗ . Put, a = and b = .
Then a b ∗ but b a ∗ So a b ∗ need not be equal to b a ∗ . Hence ∗ does not have commutative property . (iii) Next consider a b c b c ∗ ∗ ∗ ) . Take a and c = .
Then a b c ∗ ∗ ∗ ∗ But a b bc bc ∗
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