Question

If G = {7, 8} and H = {5, 4, 2}, find G × H and H × G.​

Answer 1

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Given, G = {7, 8} and H = {5, 4, 2}

We know that,

The Cartesian product of two non-empty sets P and Q is given as

P × Q = {(p, q): p ∈ P, q ∈ Q}

So,

G × H = {(7, 5), (7, 4), (7, 2), (8, 5), (8, 4), (8, 2)}

H × G = {(5, 7), (5, 8), (4, 7), (4, 8), (2, 7), (2, 8)}

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Answer 2

Answer:

(G x H) = {(7,5), (7,4), (7,2), (8,5), (8,4), (8,2)}

(H x G) = {(5,7), (5,8), (4,7), (4,8), (2,7), (2,8)}

Given:

G = {7,8}

H = {5,4,2}

To Find:

(G x H)

(H x G)

Calculating:

(G x H)

= {7,8} x {5,4,2}

= {(7,5), (7,4), (7,2), (8,5), (8,4), (8,2)}

Therefore, (G x H) = {(7,5), (7,4), (7,2), (8,5), (8,4), (8,2)}

Now Calculating for H x G:

= {5, 4, 2} x {7,8}

= {(5,7), (5,8), (4,7), (4,8), (2,7), (2,8)}

Therefore, (H x G) = {(5,7), (5,8), (4,7), (4,8), (2,7), (2,8)}