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.

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

can some one figure it out plz

Answer 1

Are these --> 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.

what you mean by "the following two statements?"

Answer 2

If so, are these answer options:

The number is a multiple of 8.
If a number is a multiple of 64, then it is a multiple of 2.
The number is a multiple of 2.
If a number is not a multiple of 2, then the number is not a multiple of 64
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I cannot decipher where the question ends.

Answer 3

it ends at the 2

Answer 4

the first 2 in the sentence

Answer 5

did u get it

Answer 6

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 7

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 8

Assumption:

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.

Answer 9

The contrapositve of an implication and the implication are logically equivalent. They are two ways to say the same thing.

p --> r and ~r --> ~p are contrapositives.

The contrapostive of p -->r is, in words for this problem, If a number is not a multiple of 2, then the number is not a multiple of 64.

Answer 10

Because of the way the problem is posted as a run-on sentence with no clear demarcation between question and answer options, I am not confident that I have interpreted the question, whatever it was, correctly.