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Problem 11

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

Expert verified
The number of elements in the Cartesian product of sets B and C is 18.
See the step by step solution

## Step 1: Find the number of elements in each set.

We have to find the number of elements in sets B and C. Set B has 6 elements since it contains numbers from 1 to 6, and set C has 3 elements since it contains 3 colors: red, green, and blue.

## Step 2: Calculate the Cartesian product

The Cartesian product of two sets, B and C, is defined as the set of all ordered pairs formed by combining each element from set B with each element in set C. The formula to calculate the number of elements in the Cartesian product is: Number of Elements in Cartesian product = Number of elements in set B * Number of elements in set C

## Step 3: Calculate n(B x C)

We now substitute the values we found in step 1 into the formula from step 2: n(B x C) = Number of elements in set B * Number of elements in set C n(B x C) = 6 * 3

## Step 4: Find the result

Multiplying the numbers we obtained in step 3: n(B x C) = 18 There are 18 elements in the Cartesian product of sets B and C.

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