The truth table represents the statements…

Maths Questions

The truth table represents the statements p, q, and r as follows: p q r A T T T B T T F C T F T D T F F E F T T F F T F G F F T H F F F Which statements are true for rows A and E? Check all that apply: 1. p ‚àß q 2. p ‚àß r 3. q ‚àß p 4. q ‚àß r 5. r ‚àß p 6. r ‚àß q

Answer

The true statements for truth table rows A and E are: p ‚Üî q, p ‚Üî r, q ‚Üî p, q ‚Üî r, r ‚Üî q. To analyze the truth values in rows A and E, we find: Row A: p = T, q = T, r = T; Row E: p = F, q = T, r = T. Now, let’s assess each logical equivalence: p ‚Üî q (p if and only if q): A: T ‚Üî T is True; E: F ‚Üî T is False. p ‚Üî r (p if and only if r): A: T ‚Üî T is True; E: F ‚Üî T is False. q ‚Üî p (q if and only if p): A: T ‚Üî T is True; E: T ‚Üî F is False. q ‚Üî r (q if and only if r): A: T ‚Üî T is True; E: T ‚Üî T is True. r ‚Üî p (r if and only if p): A: T ‚Üî T is True; E: T ‚Üî F is False. r ‚Üî q (r if and only if q): A: T ‚Üî T is True; E: T ‚Üî T is True. Thus, the true statements for rows A and E are: p ‚Üî q, p ‚Üî r, q ‚Üî p, q ‚Üî r, and r ‚Üî q.

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