(40 pts) Consider the transitivity of the biconditional: ((P HQ ) ^ ( Q R ))...
5 points Show that p + (q + r) and q + (pvr) are logically equivalent without using a truth table. To get full credit, include which logical equivalences you used.
3. Show that the following argument with hypotheses on lines 1-3 and conclusion on line c is valid by supplementing steps using the rules of inference (Rosen, page 72) and logical equivalences (Rosen, pages 27, 28). Clearly label each step. 1 pv (r 18) Premise 2 p → Premise Premise 39 Conclusion
Let p and q be the following statements. p: Ravi is going to work on Monday. q: We are going to the museum. Consider this argument Premise 1: If Ravi is going to work on Monday, then we are going to the museum. Premise 2: Ravi is not going to work on Monday. Conclusion: Therefore, we are not going to the museum. (a) Write the argument in symbolic form. Premise 1: р 9 Premise 2: 0 Conclusion: - 0 DAD...
Problem 3.11 Show using a chain of logical equivalences that (p → r)A(q → r) pv q) →
Verify the logical equivalences using the theorem below: (p ∧ ( ~ ( ~ p ∨ q ) ) ) ∨ (p ∧ q) ≡ p Theorem 2.1.1 Let p, q, and r be statement variables, t a tautology, and c a contradiction. The following logical equivalences are true. 1. Commutativity: p1q=q1p; p V q = 9VP 2. Associativity: ( pq) Ar=p1qAr); (pVq) Vr=pv (Vr) 3. Distributivity: PA(Vr) = (p19) (par); p V (qar) = (pVg) (Vr) 4. Identity: pAt=p:...
3. (10 pts.) Use logical equivalences to show that (p r)v(q r) and (pAq) r ane logically equivalent.
Prove the following is a tautology (without using a truth table) [(p →q) (q + r)] → (p → r)
QUESTION 3 Symbolize the following argument using the variables p, q, and r. Then construct a complete truth table to show whether or not the argument is valid. Use 1 for T(true) and 0 for F(false). Valid or Invalid? Why? Prove. Explain what your truth table shows. 10 points Total: 3 points for correct symbolic form, 4 points for valid/invalid and reason, 3 points for correct truth table. If Max studies hard, then Max gets an 'A' or Max gets...
3. (Logic) Answer the following questions: Construct the truth table for (p rightarrow r) (q rightarrow r) doubleheadarrow (p q) rightarrow r Is the following argument valid? (r s) (q s) s rightarrow (p r) rightarrow t) t rightarrow (s r) p rightarrow r
answer. A4 Consider a formal argument which has two premises: “p implies not q”, and “p or not q”, with the conclusion that “q is false”. a. Is this a valid argument? Give a truth table that verifies your b. Convert the statement “any integer less than C is also less than Cz" into “r implies s” form: i.e. what are the statements r and s? (Remember to substitute your integer values of C and C3.) c. Fix any integer...