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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.
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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.
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
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.