Answer and Step-by-step explanation:
1.
First, we need to find what numbers 5 and 7 both go into, and are 2-digits.
5 and 7 go into the numbers 35 and 70.
So, that means the amount of numbers 5 and 7 go into and are 2-digits is Two Numbers.
2.
Now, we have to find the amount of numbers 5 goes into and the amount of numbers 7 goes into, and they need to be 2-digits.
5 goes into the numbers 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, and 95. -- 18 numbers
7 goes into the numbers 14, 21, 28, 35, 42, 49, 56, 63, 70, 77, 84, 91, and 98. -- 13 numbers.
n(A) = 18 n(B) = 13
Now, the set of 2-digit numbers that are multiples of both 5 and 7 is given by
A∩B = {35, 70} ⇒ n(A∩B) = 2
Therefore, the number of 2-digit numbers that are multiples of either 5 or 7 is given by
n(A∪B) = n(A) + n(B) - n(A∪B) = 18 + 13 - 2 = 29
Now, there are 90 2 -digit numbers.
Thus, the number 2-digit numbers are multiples of neither 5 nor 7 is
90 - 29 = 61.
Hence, the total number of numbers is 61.
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