Suppose P, Q and R are atomic propositions. (a) Show that the conjunction connective satisfies the...

Suppose P, Q and R are atomic propositions.

(a) Show that the conjunction connective satisfies the commutative and associativity property.

(b) Show that the disjunction connective satisfies the commutative and associativity property.

(c) Construct a propositional form using all three atomic propositions above as well as the connectives conjunction, disjunction and conditional.

(d) Construct an equivalent propositional form for (c).

Expert Solution

Colby Messinger answered 6 months ago

Let p and q be propositions. (i) Show (p →q) ≡ (p ∧ ¬q) →F (ii.)...

Let p and q be propositions. (i) Show (p →q) ≡ (p ∧ ¬q) →F (ii.) Why does this equivalency allow us to use the proof by contradiction technique?

FOR EAICH PAIR OF PROPOSITIONS P AND Q STATE WHETHER ON NOT p=q p=(s→(p ∧¬r)) ∧...

FOR EAICH PAIR OF PROPOSITIONS P AND Q STATE WHETHER ON NOT p=q p=(s→(p ∧¬r)) ∧ ((p→(r ∨ q)) ∧ s), Q=p ∨ t

Show that if P;Q are projections such that R(P) = R(Q) and N(P) = N(Q), then...

Show that if P;Q are projections such that R(P) = R(Q) and N(P) = N(Q), then P = Q.

A list of six positive integers, p, q, r, s, t, u satisfies p < q...

A list of six positive integers, p, q, r, s, t, u satisfies p < q < r < s < t < u. There are exactly 15 pairs of numbers that can be formed by choosing two different numbers from this list. The sums of these 15 pairs of numbers are: 25, 30, 38, 41, 49, 52, 54, 63, 68, 76, 79, 90, 95, 103, 117. Which sum equals r + s?

1.) Suppose that the statement form ((p ∧ ∼ q)∨(p ∧ ∼ r))∧(∼ p ∨ ∼...

1.) Suppose that the statement form ((p ∧ ∼ q)∨(p ∧ ∼ r))∧(∼ p ∨ ∼ s) is true. What can you conclude about the truth values of the variables p, q, r and s? Explain your reasoning 2.Use the Laws of Logical Equivalence (provided in class and in the textbook page 35 of edition 4 and page 49 of edition 5) to show that: ((∼ (p ∨ ∼ q) ∨ (∼ p ∧ ∼ r)) ∧ s) ≡ ((r...

Suppose S = {p, q, r, s, t, u} and A = {p, q, s, t}...

Suppose S = {p, q, r, s, t, u} and A = {p, q, s, t} and B = {r, s, t, u} are events. x p q r s t u p(x) 0.15 0.25 0.2 0.15 0.1 (a) Determine what must be p(s). (b) Find p(A), p(B) and p(A∩B). (c) Determine whether A and B are independent. Explain. (d) Arer A and B mutually exclusive? Explain. (e) Does this table represent a probability istribution of any random variable? Explain.

Suppose that ?: ℝ → (0, ∞) satisfies ?(? + ?) = ?(?)?(?). Show that if...

Suppose that ?: ℝ → (0, ∞) satisfies ?(? + ?) = ?(?)?(?). Show that if ? is continuous at 0, then there is an ? ∈ (0, ∞) such that ?(?) = ?^x for all ? ∈ ℝ.

Prove p → (q ∨ r), q → s, r → s ⊢ p → s

Use rules of inference to show that the hypotheses p → q, r → s, and...

Use rules of inference to show that the hypotheses p → q, r → s, and ¬q ∨ ¬s implies ¬p ∨ ¬r

Two compound propositions p and q in propositional logic are logically equivalent if . . ..

Complete the following statements.Two compound propositions p and q in propositional logic are logically equivalent if . . ..An argument form in propositional logic is valid if . . ..A theorem is a statement that . . ..A statement that is assumed to be true is called a(n) . . ..A proof is a valid argument that . . ..

Question