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 C) Modus Tollens D) Constructive Dilemma

6. Match each logical statement in the left hand column with an equivalent logical statement in the right hand column. Logical Statement (i) ~ WA~y Logical Statement (v) w v ~y (ii) wA~y (vi) ~ (~w→ y) (iii) w v y (vii) ~ (~w v y) (viii) ~ w → y (iv) ~ (~WAy)

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2

Second question pls

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

Part I Each of the following is a formal proof of validity for the indicated argument. State the justification for each line that is not a premise (for each line that is in bold type). A) 1. Tv (E → D) 2. T → C 3. (~T~C) → (D → G) 4. ~C 5. T 6. E → D 7. ~T~C 8. D→ G 9. E → G B) 1. S→ (~T→→ U) 2. U →~U 3. (S~T) → U 4. -Uv U 5. ~U 6. ~(ST) .. E → G :. ~SVT 1. (~Tv R) • (~Tv S) 2. ~P~(P v Q) 3. P 4. [~P~(P v Q)] • [~(P v Q) →~P] 5. (P v Q)→→~P 6. P→ (PvQ) 7. P→ (Q v P) 8. ~Tv (RS) 9. T (R.S) 10. PVT .. Q v [P v (RS)] 11. (Q v P) v (R.S) 12. Q v [Pv (R•S)]

Argument 5: Premise: Premise: Conclusion: Argument Form? Argument 6: Premise: (C 5 J) • (~P = W) Premise: Cv mP Conclusion: ~) v W Argument Form? Argument 7: Premise: Premise: Conclusion: Argument Form? Argument 8: Premise: Premise: Conclusion: Arqument Form?

Which option below (a,b,c, or d) represents the small world that this inference being made is NOT valid.Inference= (∀x)(Fx->Gx) and Fa; therefore, (∀x)Gx.a) Individuals: a, b; Predicates: Gbb) Individuals: a, b; Predicates: Fa, Fb, Ga, Gbc) Individuals: a, b; Predicates: Fa, Ga, Fbd) Individuals: a, b; Predicates: Fa, Ga