Question 3 of 33beginner🔧 ApplyShort Answer2 marks

If G={7,8}G = \{7, 8\} and H={5,4,2}H = \{5, 4, 2\}, find G×HG \times H and H×GH \times G.

Correct Answer

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)}

Exercise: EXERCISE 2.1 | Q: 3 | (Page 4)
For More Understanding

Explanation

This question tests the understanding of Cartesian products. From the context, the Cartesian product A × B consists of all ordered pairs (x, y) where x ∈ A and y ∈ B. The example in the context shows that for A = {a₁, a₂} and B = {b₁, b₂, b₃, b₄}, the product A × B lists all combinations with first element from A and second from B. Applying this: G × H has 2×32 \times 3 = 6 ordered pairs with first element from G and second from H. Similarly, H × G has 3×23 \times 2 = 6 ordered pairs with first element from H and second from G. Note that G × H ≠\neq H × G as ordered pairs are not commutative.

Solution Steps

  1. Step 1: For G × H, take each element of G = {7, 8} and pair with each element of H = {5, 4, 2}

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

  3. Step 3: For H × G, take each element of H = {5, 4, 2} and pair with each element of G = {7, 8}

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

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