Question

Read the following two statements. Then use the Law of Syllogism to draw a conclusion.

If a number is a multiple of 64, then it is a multiple of 8.
If a number is a multiple of 8, then it is a multiple of 2.

a. The number is a multiple of 8.
b.If a number is a multiple of 64, then it is a multiple of 2.
c.The number is a multiple of 2.
d. If a number is not a multiple of 2, then the number is not a multiple of 64.

Answer 1

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Answer 2

Using symbolic logic:
Let p represent: a number is a multiple of 64
q represent: the number is a multiple of 8.

So, If a number is a multiple of 64, then it is a multiple of 8 translates symbolically to:

P -->q which is read p implies q, or If p, then q.

Answer 3

Looking at the second given implication:
If a number is a multiple of 8, then it is a multiple of 2.
-------------
Once again,
q represents: the number is a multiple of 8.

and Let r represent
the number is a multiple of 2

Then, the second implicated is represented symbollically as:

q -->r

Answer 4

If a number is a multiple of 64, then it is a multiple of 8.

If a number is a multiple of 8, then it is a multiple of 2.
is the given information

Therefore, from above

(1) p -->q
and
(2) q -->r
Therefore, p -->r.

Coding back for what p and r represent:
Conclusion:

If a number is a multiple of 64, then it is a multiple of 2.