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Let p represent "B is between A and C" and q represent "A, B, and C are collinear." Which symbolic statement represents the conditional statement "If B is not between A and C, then A, B, and C are not collinear"?

A. ~p → ~q
B. p → q
C. ~q → ~p
D. q → p

User Neyda
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1 Answer

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Final answer:

The correct symbolic representation for the conditional statement 'If B is not between A and C, then A, B, and C are not collinear' is 'A. ¬p → ¬q'.

Step-by-step explanation:

The conditional statement "If B is not between A and C, then A, B, and C are not collinear" is represented by the symbolic statement ¬p → ¬q. Here's why: p represents the statement "B is between A and C," and q represents "A, B, and C are collinear." The negation of p, ¬p, corresponds to "B is not between A and C," and the negation of q, ¬q, represents "A, B, and C are not collinear." The conditional ¬p → ¬q matches the structure of a conditional statement, which is often used to describe logical relationships between propositions. Therefore, the correct answer is A. ¬p → ¬q.

User Norrius
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