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Question: can you answer the question 14 thanks...

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Can you answer the question 1-4, thanks!

1. Let p, q, and r be propositions. (i) Make the truth tables for-p V q) and (гр) Λ (-y) to show that they are equiv- alent. (ii) Make the truth tables for-png) and (mp) V (y) to show that they are equiv- alent. (iii) Make the truth table for ﹁(mp) to show that C﹁p)) p (iv) Use (1-11) and start with pVq (rather than with (mp) → q) to derive the fact that (p V q) ((mp) q). (Here derive means by the use of a succession of (v) Use (1-111) and start with (pV q) r (rather than with (p r) Л (q r)) to (vi) Use (1-111) and start with (p Л q) r (rather than with (p r) V (q r)) to (vii) Use (1-111) and start with p → (q Vr) (rather than with (рл (-q)) → r) to derive (vii) Use (i-ii) and start with p -(Vr) (rather than with (p - ) V (p-T) to s rather than by making the truth tables.) derive the fact that ((pv q) r) t+ (p r) Λ (q r)) derive the fact that ((pA q) r) ((p r) V (q r)). the fact that (p (q V r)) ( (p л (-q)) r) derive the fact that (p → (q V r)) ( (p → q) V (p → r) derive the fact that (p → (q Λ r))艹((p → q) Λ (p → r)). definition restatement p (ix) Use (1-111) and start with p → (q Λ r) (rather than with (p → q) Λ (p → r)) to (x) Use (i-iii) to find-p → q). (Your final answer should not be simply its by-

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