Question

if two sets A and B have 17 in common then the number of elements common to the AxB and BxA is ​

Answer 1

SOLUTION

GIVEN

Two sets A and B have 17 in common

TO DETERMINE

The number of elements common to the A × B and B × A

EVALUATION

We know that for two sets A and B their cartesian product is denoted by A × B and defined as

A × B = { (a, b) : a ∈ A ∧ b ∈ B }

Now it is given that A and B have 17 in common

∴ n (A ∩ B) = 17

∴ The number of elements common to the A × B and B × A

= n [ (A × B) ∩ (B × A) ]

= n(A ∩ B) × n(B ∩ A )

= 17 × 17

= 289

FINAL ANSWER

The number of elements common to the A × B and B × A = 289

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