Determine the line and the reason for the entry on line 5 given the following part of a formal proof of validity: 1. (P= Q) A (R= S) РAR 2. 3. P = Q 4. 5. 6. (R= S) ^ (P → Q) A 3,4 MODUS PONENS B 1,2 CONSTRUCTIVE DILEMMA 1 SIMPLIFICATION D 1,2 DESTRUCTIVE DILEMMA

Which postulate justifies that ДНАМ-ДСОW? H. а. АА C. ASA b. SSA d. SAS

I have to prove that the answer is right using inference laws

4) If is a real numbes and Tumber 1 1t 2 +3 3+1 I represented on the Argand dia goea by a point line show thet a

7. Use all of the premises to determine a alid conclusion for the following argument. ~m Vt t → -d e Vg e → d ..?

Use therules of implicationand replacement to derive the conclusions of the following symbolized arguments. (All work must be shown) 1. M ˅ P 2. (P ˅ S) ⊃ (R • D) 3.  M                / R

State the rule of inference by which its conclusion follows from its premise or premises. (H ɔ (I = J)) v (E v F) - (H ɔ (I = J)) .: (E v F) A Modus Ponens B Disjunctive Syllogism Modus Tollens Constructive Dilemma

4.) 5.) 6.)

2. Let p, q, and r be as in Exercise 1. Translate the follow- ing into English sentences. (a) (p ^ q) → r (c) p (q vr) (e) (pvq) ^r (b) (pr)→ 9 (d) (p → (q vr))