For each of the following formulas, list the values of the formula under every assignment, state if the formula is valid or not, and state if the formula is sat- isfiable or not. The ordering of the assignments and format for the answers is below. 1. (p→q) →(q→p) 2. (p↔(q↔r)) 3. (p(qr)) ((p↔q) ↔r) Your answer to each formula should be on a separate line in the following for- mat: list the values of the formula for the assignments in the usual order, fol- lowed by either VALID or NOTVALID, followed by either SAT or NOTSAT. So, for formulas with variables p, q, the order is 00 01 10 11, and for formulas with variables p, q, r, the order is 000 001 010 011 100 101 110 111. For example, for the formula p^ q the answer would be: 0 0 0 1 NOTVALID SAT
For each of the following formulas, list the values of the formula under every assignment, state if the formula is valid or not, and state if the formula is sat- isfiable or not. The ordering of the assignments and format for the answers is below. 1. (p→q) →(q→p) 2. (p↔(q↔r)) 3. (p(qr)) ((p↔q) ↔r) Your answer to each formula should be on a separate line in the following for- mat: list the values of the formula for the assignments in the usual order, fol- lowed by either VALID or NOTVALID, followed by either SAT or NOTSAT. So, for formulas with variables p, q, the order is 00 01 10 11, and for formulas with variables p, q, r, the order is 000 001 010 011 100 101 110 111. For example, for the formula p^ q the answer would be: 0 0 0 1 NOTVALID SAT
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:For each of the following formulas, list the values of the formula under every
assignment, state if the formula is valid or not, and state if the formula is sat-
isfiable or not. The ordering of the assignments and format for the answers is
below.
1. (p→→q) →(q→p)
2. (p↔(q↔r))
3. (p↔(q↔r)) ↔((p↔q) ↔r)
Your answer to each formula should be on a separate line in the following for-
mat: list the values of the formula for the assignments in the usual order, fol-
lowed by either VALID or NOTVALID, followed by either SAT or NOTSAT.
So, for formulas with variables p, q, the order is 00 01 10 11, and for formulas
with variables p, q, r, the order is 000 001 010 011 100 101 110 111.
For example, for the formula p^q the answer would be:
0 0 0 1 NOTVALID SAT
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