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Problem 10

# Let $$A=\\{\mathrm{H}, \mathrm{T}\\}, B=\\{1,2,3,4,5,6\\},$$ and $$C=\\{$$ red, green blue $$\\}$$. Find the numbers indicated. $$n(B \times B)$$

Expert verified
The number of elements in the Cartesian product of set B with itself (B x B) is 36.
See the step by step solution

## Step 1: Determine the number of elements in set B

Count the elements in set B to determine its size. Set B has six elements: {1,2,3,4,5,6}. Therefore, the number of elements in set B is 6.

## Step 2: Calculate the Cartesian product of set B with itself

Since we need to find the number of elements in the cartesian product of B and B (B x B), multiply the number of elements in set B (which is 6) by itself: $$6 \times 6$$.

## Step 3: Calculate the result

Multiply the number of elements in set B by itself: $$6 \times 6 = 36$$.

## Step 4: Write the final answer

The number of elements in the cartesian product of set B with itself (B x B) is 36.

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