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Question Number 57822 by 1103264451 last updated on 12/Apr/19

If A and B are two non empty   equivalent sets, then a possible value  of n(A×B) is

$$\mathrm{If}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}\:\mathrm{are}\:\mathrm{two}\:\mathrm{non}\:\mathrm{empty}\: \\ $$$$\mathrm{equivalent}\:\mathrm{sets},\:\mathrm{then}\:\mathrm{a}\:\mathrm{possible}\:\mathrm{value} \\ $$$$\mathrm{of}\:{n}\left(\mathrm{A}×\mathrm{B}\right)\:\mathrm{is} \\ $$

Commented by Rasheed.Sindhi last updated on 13/Apr/19

n(A×B)=n(A)×n(B)  ∵ n(A)=n(B)  ∴ n(A×B)=n(A)×n(A)=[n(A)]^2

$${n}\left(\mathrm{A}×\mathrm{B}\right)={n}\left(\mathrm{A}\right)×{n}\left(\mathrm{B}\right) \\ $$$$\because\:{n}\left(\mathrm{A}\right)=\mathrm{n}\left(\mathrm{B}\right) \\ $$$$\therefore\:{n}\left(\mathrm{A}×\mathrm{B}\right)={n}\left(\mathrm{A}\right)×{n}\left(\mathrm{A}\right)=\left[{n}\left(\mathrm{A}\right)\right]^{\mathrm{2}} \\ $$

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