Question

In Jana's closet she has 5 pairs of black shoes and 11 pairs of leather shoes. Two of her pairs of shoes are both black and leather. Determine the total number of shoes that are either black, leather, or both.

A) 5 pairs
B) 11 pairs
C) 12 pairs
D) 14 pairs

Answer 1

i just did the test 14 is the answer

Answer 2

Answer: D) 14 pairs

Explanation:

Let B represents black shoes and L represents leather shoes.

Then,
`n(B)`=5

`n(L)`=11

`n(B\cap L)=2`

Then the total number of shoes that are either black, leather, or both. is given by :-

`n(B\cup L)=n(B)+n(L)-n(B\cap L)=5+11-2=14`

Hence, the total number of shoes that are either black, leather, or both =14