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Problem 32

# Let $$\mathrm{M}=\\{1,2\\}$$ and $$\mathrm{N}=\\{\mathrm{p}, \mathrm{q}\\} .$$ Find (a) $$\mathrm{M} \times \mathrm{N}$$ (b) $$\mathrm{N} \times \mathrm{M}$$, and (c) $$\mathrm{M} \times \mathrm{M}$$

Expert verified
(a) M x N = \{(1, p), (1, q), (2, p), (2, q)\} (b) N x M = \{(p, 1), (p, 2), (q, 1), (q, 2)\} (c) M x M = \{(1, 1), (1, 2), (2, 1), (2, 2)\}
See the step by step solution

## Step 1: (a) M x N

To find M x N, we will create ordered pairs where the first element is from set M and the second element is from set N. M = {1, 2} N = {p, q} M x N = {(1, p), (1, q), (2, p), (2, q)}

## Step 2: (b) N x M

To find N x M, we will reverse the order of the elements in the pairs. Now, the first element will be from set N and the second element will be from set M. N x M = {(p, 1), (p, 2), (q, 1), (q, 2)}

## Step 3: (c) M x M

To find M x M, we will again create ordered pairs, but in this case both elements in the pair will come from set M. M x M = {(1, 1), (1, 2), (2, 1), (2, 2)}

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