Question

Let n(A) denotes the number of elements in set A. If n(A) =p and n(B) = q, then how many ordered pairs (a, b) are there with a ∈ A and b ∈ B ?​

Answer 1

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GIVEN

• Let n(A) denotes the number of elements in set A

• n(A) =p and n(B) = q

TO DETERMINE

The number of ordered pairs (a, b) with

a ∈ A and b ∈ B

CALCULATION

If A and B are two sets. Then the Cartesian product of A and B is denoted by A × B and defined as

$\sf{A \times B = \{ \: (a, b) : a \in A \: , \: b \in \: B \: \}}$

$\sf{So \: \: \: \: n(A \times B) = n(A) .n(B) }$

Here it is given that n(A) =p and n(B) = q

Hence

$\sf {n(A \times B) = n(A) .n(B) }$

$\implies \sf{n(A \times B) = pq}$

Hence there are pq ordered pairs (a, b) with a ∈ A and b ∈ B

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LEARN MORE FROM BRAINLY

If n(A) = 300, n(A∪B) = 500, n(A∩B) = 50 and n(B′) = 350, find n(B) and n(U)

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