Math

QuestionIdentify the correct term for: If xyx \Rightarrow y and yzy \Rightarrow z, then xzx \Rightarrow z. A. Converse B. Syllogism C. Inverse D. Contrapositive

Studdy Solution

STEP 1

Assumptions1. The statement given is "If xyx \Rightarrow y and yzy \Rightarrow z, then xzx \Rightarrow z." . We need to identify which term best describes this statement.

STEP 2

Let's analyze each optionA. Converse statement This is when the hypothesis and the conclusion of a conditional statement are switched. In this case, the statement "If xyx \Rightarrow y and yzy \Rightarrow z, then xzx \Rightarrow z" does not switch any hypothesis or conclusion, so it is not a converse statement.
B. A syllogism This is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true. In this case, the statement "If xyx \Rightarrow y and yzy \Rightarrow z, then xzx \Rightarrow z" does apply deductive reasoning based on the two propositions "xyx \Rightarrow y" and "yzy \Rightarrow z" to arrive at the conclusion "xzx \Rightarrow z". So it could be a syllogism.
C. Inverse statement This is when both the hypothesis and the conclusion of a conditional statement are negated. In this case, the statement "If xyx \Rightarrow y and yzy \Rightarrow z, then xzx \Rightarrow z" does not negate any hypothesis or conclusion, so it is not an inverse statement.
. Contrapositive statement This is when both the hypothesis and the conclusion of a conditional statement are switched and negated. In this case, the statement "If xyx \Rightarrow y and yzy \Rightarrow z, then xzx \Rightarrow z" does not switch or negate any hypothesis or conclusion, so it is not a contrapositive statement.

STEP 3

Based on the analysis in2, the term that best describes the statement "If xyx \Rightarrow y and yzy \Rightarrow z, then xzx \Rightarrow z" is a syllogism.
So, the answer is B. A syllogism.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord