Q. 94.3( 6 Votes )

# If A = {(x, y) : y = e^{x}, xR} and B = {(x, y) : y = e^{−}^{x}, xR}, then write .

Answer :

Here, and

A⋂B={(x,y):y=e^{x} ,xϵR} and {(x,y):y=e^{-x} ,xϵR}

={(x,y):y= e^{x} and y= e^{-x} xϵR}

={(x,y): e^{x} = e^{-x} xϵR}

={(x,y):e^{2x} =1,xϵR}

={(0,1)} (∵ )

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Let A = {a, b, c, d}, B = {c, d, e} and C = {d, e, f, g}. Then verify each of the following identities:

(i) A × (B ∩ C) = (A × B) ∩ (A × C)

(ii) A × (B – C) = (A × B) – (A × C)

(iii) (A × B) ∩ (B × A) = (A ∩ B) × (A ∩ B)

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RS Aggarwal - MathematicsIf A and B be two sets such that n(A) = 3, n(B) = 4 and n(A ∩ B) = 2 then find.

(i) n(A × B)

(ii) n(B × A)

(iii) n(A × B) ∩ (B × A)

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(A × B) ∩ (B × A) = (A ∩ B) × (B ∩ A).

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Hint n(A) = n(A – B) + n(A ∩ B) n(A ∩ B) = (23 – 8) = 15.

RS Aggarwal - Mathematics