4. (8 Points) Using a truth table, prove the following statements are logically equivalent. Be sure...
Problem 12.1: Let p and be logical statements. By using a truth table determine if the following compound statements are logically equivalent. Show work! Circle one: A: The statements are equivalent. B: The statements are not equivalent. Problem 12.2: Let P, Q, and be be logical statements. By using a truth table determine if the following compound statements are logically equivalent. Show work! Circle one: A: The statements are equivalent. B: The statements are not equivalent.
4. Use truth tables to determine whether the following two statements are logically equivalent. (P+Q)^(~Q) and ~ (PVQ)
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.
4. (4 points) Prove the truth or falsity of the following statements. To prove a statement true, give a formal argument (in cases involving implications among FD's, use Armstrong's Axiom System). To prove falsity, give a counterexample. 1. {A + B, DB → C} F{A+C} 2. {X+W, WZ+Y} F{XZ → WY} 3. {A D, B7C, F + B, CD + E|| F{AF → E} 4. Suppose R is a relation scheme and F a set of functional dependencies applicable to...
PROVE USING TRUTH TABLE 4. (CA-B) + (-AVB)
Multiple Choice Question 1. You can recognize a contradiction from the statement's truth table because: A. It is not possible to recognize a contradiction from the truth table. B. Most of the entries in the final column will be "true".. C. The entries in the final column will all be "false". D. Most of the entries in the final column will be "false". E. The entries in the final column will all be "true". Question 2 You are writing a...
Give an example of a predicate P(x, y) such that the following two statements are logically equivalent: Vx3yP(x, y) and 3xVyP(x, y)
Please upload a picture of your work. For problems 1-3 complete the truth table for the following statements and determine if they are logically equivalent. For 4-6 use a truth table to determine if the argument is valid. 1.-(PAQ) and Pv-Q 2. P-Q and QP 3.P-Q and -PVQ 4.P-Q 5. ( PQ) - Q P 6. PvQ QR PVR FB I U
Prove or disprove the following expression. (Prove: using Boolean algebra. Disprove: using truth table.) (NOT is presented by -.) 1. a + b (c^- + d)^- = a^-b^- + a^-cd^- 2. ab^- + bc^- + ac^- = (a + b + c) (a^- + b^-+ c^-) 3. a^- + bd^-^- (c + d) + ab^-d = ac^-d + ab^-cd + abd
Using ONLY logical equivalences (not truth tables!), prove for the following that one element of the pair is logically equivalent to the other one using logical equivalences (ex. De Morgan's laws, Absorption laws, Negation laws etc.) a) ~d -> (a && b && c) = ~(~a && ~d) && ((d || b) & (c || d)) b) (a->b) && (c->d) = (c NOR a) || (b && ~c) || (d && ~a) || (b && d) c) (~a && ~b)...