Select the logical expression that is equivalent to: -Vx3y(P(2) A Q(x,y)) Vydt-P(1) V-Q(x,y)) yV:( P(1) VQ(x,y))...
Select the logical expression that is equivalent to: 3x(P(2) AQ(x)) ( P(x) V-Q(x)) Vo(-P(x)^-Q(x)) V«(- P() V-Q()) O 3:(-P(x)^-Q(:))
Is P(x) V(x) equivalent to x(P(x) V Q(x))? Explain Is P(x) V(x) equivalent to x(P(x) V Q(x))? Explain
Express each English statement using logical operations V, Lambda, - 1. and the propositional variables t, n, and m defined below. The use of the word "or" means inclusive or. t: The patient took the medication. n: The patient had nausea. m: The patient had migraines. There is no way that the patient took the medication. a) -n b) -(-m) c) -m d) -t Define the following propositions: s: a person is a senior. y: a person is at least...
3. (10 pts.) Use logical equivalences to show that (p r)v(q r) and (pAq) r ane logically equivalent.
20. Let u = (2).= (1) and w = (1) . If ou+yv=w, (x, y € R), then x + y = (A) 1/5 (B) 2/5 (C) 1 (D) 4/5 (E) 3/5
Determine the domain of each of the functions P(x), Q(x), V(x), and Z(x). Select the one row that gives the correct domain underneath each function. P(x)= x2 + 1 Q(x) = Ne + 1 V(r) = **1 Z(x) = log (x + 1) OP: [-1, )Q: (-00, -1) (-1,00) V:(-0,0) Z: (-1,00) OP: (-00,00) Q: (-1,0) V: (-00, -1) (-1,0) Z: (-1,00) OP: (-00,00) Q: (-1,-) V: (-0, -1) U (-1,00) Z: (-1,0) OP: (-0, -1) U (-1,0) Q: (-1,-)...
Use Python to determine whether below expression is satisfiable. (p V -q) ~ (q V - r) ~ (r V -p) ~ (p V q V r) ~ (-p V -q V -r)) Find the output of the below FOUR circuits r-
2. (a) Show that (PVQ) + R is not logically equivalent to (P + R) V(Q + R) using a truth table. (b) Is (PAQ) → R logically equivalent to (P + R) A( Q R )? If so, use a truth table to establish this. If not, show that it is false.
Predicates P and Q are defined below. The domain of discourse is the set of all positive integers. P(x): x is prime Q(x): x is a perfect square (i.e., x = y2, for some integer y) Find whether each logical expression is a proposition. If the expression is a proposition, then determine its truth value. 1) ∃x Q(x) 2) ∀x Q(x) ∧ ¬P(x) 3) ∀x Q(x) ∨ P(3)
Assume that p NAND q is logically equivalent to ¬(p ∧ q). Then, (a) prove that {NAND} is functionally complete, i.e., any propositional formula is equivalent to one whose only connective is NAND. Now, (b) prove that any propositional formula is equivalent to one whose only connectives are XOR and AND, along with the constant TRUE. Prove these using a series of logical equivalences.