what is a counterexample for the conjecture?
conjecture any number that is divisble by 2 is also divisible by 4
a.32
b.12
c.40
d.18
@ms.sue can i please have help anyone
18 = 2*9
so it is 18
To find a counterexample for the conjecture, we need to find a number that is divisible by 2 but not divisible by 4.
The conjecture states that any number divisible by 2 is also divisible by 4, so we are looking for a number that goes against this statement.
Let's go through the options provided:
a. 32: This number is divisible by both 2 and 4, so it supports the conjecture.
b. 12: This number is divisible by 2, but it is also divisible by 4 (12/4 = 3). So it does not serve as a counterexample.
c. 40: This number is divisible by both 2 and 4, so it supports the conjecture.
d. 18: This number is divisible by 2, but it is not divisible by 4 (18/4 = 4.5). Therefore, it serves as a counterexample.
Therefore, the counterexample for the conjecture is d. 18.
To find a counterexample for a conjecture, you need to provide an example that disproves the statement. In this case, the conjecture states that any number divisible by 2 is also divisible by 4. To find a counterexample, we need to find a number that is divisible by 2 but not divisible by 4.
Let's go through the options you provided:
a. 32: This number is divisible by both 2 and 4, so it does not work as a counterexample.
b. 12: This number is divisible by 2 but is also divisible by 4. Therefore, it does not work as a counterexample either.
c. 40: Again, this number is divisible by both 2 and 4, so it is not a counterexample.
d. 18: This number is divisible by 2, but it is not divisible by 4. Therefore, it works as a counterexample.
So, the counterexample for the conjecture is d. 18. This number is divisible by 2 but not divisible by 4, thus disproving the conjecture.