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Equivalent forms of a conditional statement in words ('only if', 'or', necessary condition)

This type of question, asked 3 times: May 2021 S1, 2 May 2023 S1, 11 May 2023 S1. All 3 questions below, oldest first.

Try each one first, then open its answer.

  1. Question 1

    May 2021 S1

    114
    Consider the following statements: r: If a number is a multiple of 9, then it is a multiple of 3. Let pp: A number is a multiple of 9, and qq: A number is a multiple of 3. Then, 'if p then q' is the same as

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  2. Question 2

    2 May 2023 S1

    140
    If statement I: If the work is not finished on time, the contractor is in trouble. Statement II: Either the work is finished on time or the contractor is in trouble. Then

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  3. Question 3

    11 May 2023 S1

    112
    Let p, q and r be the statements: p: X is an equilateral triangle; q: X is isosceles triangle; r:q∨∼pr: q \vee \sim p, then the equivalent statement of r is

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