Help with counterexamples, please

1. Which of the following is a counterexample to the statement “All numbers with a zero in the ones place are divisible by 5”?
A. 10
B. 40
C. 100
D. This statement does not have a counterexample.

2. Which of the following is a counterexample to the statement “All even numbers are divisible by 4”?
A. 2 x 2 = 4
B. 7 is not divisible by 4.
C. 8 is divisible by 4.
D. 10 is not divisible by 4.

3. Only false statements have counterexamples.
True or False?

4. All statements have counterexamples.
True or False?

Thank you! (:

1. None of those are counterexamples (D)
2. 10 is not divisible by 4, so it is a counterexample. (D)
3. True
4. False

1. Which of the following is a counterexample to the statement “All numbers with a zero in the ones place are divisible by 5”?
answer is D since choice a,b,c are divisible by 5


2. Which of the following is a counterexample to the statement “All even numbers are divisible by 4”?
if number is not divisible by 4, then all numbers are not even (odd)
choice B since 7 is not divisible by 4

3. Only false statements have counterexamples.
true

4. All statements have counterexamples.
false since if statemet is true, then there will be no counterexamples

To do these examples you need to look at the factors:
!. The prime factors of 10 are 2 and 5. All numbers with a 0 in the units column, other than 0, are multiples of 10, and thus are divisible by 10. Hence all these numbers are divisible by 5. Answer D.

2 The factors of 10 are 5 and 2. If you divide 10 and 4 by 2, you finish up with 5 and 2. 5 is not divisible by 2, so 10 is not divisible by 4.

3 and 4 are matters of definition. Look at 1 and 2, to see what a counterexample is.

1. D
2. D
3. True
4. False