(a)
p | q | p | q | pq |
1 | 1 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 0 |
0 | 1 | 1 | 0 | 0 |
0 | 0 | 1 | 1 | 1 |
proposition is
(b)
p | q | r | -- | p | q | r | pq | pr | qr | |
1 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
1 | 1 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 |
0 | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 0 | 1 |
0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 0 | 1 |
0 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
proposition is
(c)
p | q | r | p | pq | pr | |
1 | 1 | 1 | 0 | 0 | 1 | 0 |
1 | 1 | 0 | 0 | 0 | 0 | 0 |
1 | 0 | 1 | 0 | 0 | 1 | 0 |
1 | 0 | 0 | 0 | 0 | 0 | 0 |
0 | 1 | 1 | 1 | 1 | 0 | 0 |
0 | 1 | 0 | 1 | 1 | 0 | 0 |
0 | 0 | 1 | 1 | 0 | 0 | 0 |
0 | 0 | 0 | 1 | 0 | 0 | 0 |
proposition is
(a) Find a proposition using only p, q,-, and the connective with the truth table below....
Find the truth value of the statement. Assume that p and q are false, and r is true. 15) -(19) ►-9 A) True B) False Use a truth table to decide if the statements are equivalent. 16) q→P; - Vp A) Not equivalent B) Equivalent
Answer the following questions in the space provided below. 1. For each proposition below, first determine its truth value, then negate the proposition and simplify (using DeMorgan's laws) to eliminate all – symbols. All variables are from the domain of integers. (a) 3x, 22 <2. (b) Vx, ((:22 = 0) + (x = 0)). (e) 3xWy((x > 0) (y > 0 + x Sy)). 2. Consider the predicates defined below. Take the domain to be the positive integers. P(x): x...
Determine whether the truth table for the following compound proposition is correct or incorrect. P ⊃ (Q v R)
number 3 please 3. (a) If pA~q is true, determine the truth values of p and q. (b) If~p Vq is false, determine the truth values of p and q 4. Write pAq as an equivalent statement without using the connective A
Given p is true, q is false, and r is false, find the truth value of the statement (q ^~r) ->~p.
true and false propositions with quantifiers. Answer the following questions in the space provided below. 1. For each proposition below, first determine its truth value, then negate the proposition and simplify (using De Morgan's laws) to eliminate all – symbols. All variables are from the domain of integers. (a) 3.0, x2 <. (b) Vr, ((x2 = 0) + (0 = 0)). (c) 3. Vy (2 > 0) (y >0 <y)). 2. Consider the predicates defined below. Take the domain to...
~PVQ (Q -- P) → (PV) 7. Fill in the truth table for the statement below. Р Q ~P Q+P T T T F F T F F
1. Use a truth table in canonical form below to show that ¬p∧q and ¬p∧¬q are not equivalent. Feel free to make necessary adjustments to the table. p q p∧q ¬p ¬q ¬p∧q ¬p∧¬q 2. Tell whether the following two expressions are equivalent by constructing their truth tables in canonical form. You may make necessary adjustments to the table provided below. Is p∨q∧rlogically equivalent to p∨q∧p∨r? p q r q∧r p∨q p∨r 3. Prove or Disprove (make sure to show...
SUPER-LONG TRUTH TABLE METHOD Determine the validity using the super-long truth table method. P>~Q,~Q>~(R&S):P>(~R&~S)
Problem 1.3. (a) Verify by truth table that ( P Q ) V(QP) (1.2) is valid (b) A propositional statement is satisfiable if and only if there is an assignment of truth values to its variables which make the statement true. Explain why PE-P (1.3) is not satisfiable. (c) A set of propositional formulas P, ..., Pk is consistent if and only if there is an environment in which they are all true. Write a formula, S, so that the...