Q. 11 B5.0( 2 Votes )

# Let S = {a, b, c} and T = {1, 2, 3}. Find F^{–1} of the following functions F from S to T, if it exists.

F = {(a, 2), (b, 1), (c, 1)}

Answer :

It is given that S = {a, b, c} and T = {1, 2, 3}

F: S → T is defined as:

F = {(a, 2), (b, 1), (c, 1)}

= > F(b) = 1, F(c) = 1, F is not one-one.

Therefore, F is not invertible

⇒ F^{-1} does not exists.

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PREVIOUSLet S = {a, b, c} and T = {1, 2, 3}. Find F–1 of the following functions F from S to T, if it exists.F = {(a, 3), (b, 2), (c, 1)}NEXTConsider the binary operations ∗: R × R → R and o: R × R → R defined as a ∗b = |a – b| and a o b = a, ∀ a, b ∈ R. Show that ∗ is commutative but not associative, o is associative but not commutative. Further, show that ∀a, b, c ∈ R, a ∗ (b o c) = (a ∗ b) o (a ∗ c). [If it is so, we say that the operation ∗ distributes over the operation o]. Does o distribute over ∗? Justify your answer.

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