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Claim. There are exactly two truth environments (assignments) for the variables M, N, P, Q, R, S that satisfy the following formula: (POR Q) AND ( OR R) AND (R OR S) AND (S OR P) AND M AND N clause (1) clause (4) clause (2) clause (3) (a) This claim could be proved by truth-table. How many rows would the truth table have?

Claim. There are exactly two truth environments (assignments) for the variables M, N, P, Q, R, S that satisfy the following formula: (POR Q) AND ( OR R) AND (R OR S) AND (S OR P) AND M AND N clause (1) clause (4) clause (2) clause (3) (a) This claim could be proved by truth-table. How many rows would the truth table have?

Advanced Engineering Mathematics
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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Discrete Math
Math. Proofs and sets Claim. There are exactly two truth environments (assignments) for the variables M, N, P, Q, R, S that satisfy the following formula: (POR Q) AND (OR R) AND (R OR S) AND (S OR P) AND M AND N clause (1) clause (2) clause (3) clause (4) (a) This claim could be proved by truth-table. How many rows would the truth table have?
Transcribed Image Text:Math. Proofs and sets Claim. There are exactly two truth environments (assignments) for the variables M, N, P, Q, R, S that satisfy the following formula: (POR Q) AND (OR R) AND (R OR S) AND (S OR P) AND M AND N clause (1) clause (2) clause (3) clause (4) (a) This claim could be proved by truth-table. How many rows would the truth table have?
C(2) a2n+1 Tn P2n+1 an+2 an+1 (n+1)-bit add1 C(1) ri To 2(n+2)-bit addl module Figure 3.1 Pn+2 Pn+1 an Pn a₁ ao (n+1)-bit add1 Structure of a Double-size add1 Module. PI Po (b) Instead of a truth-table, prove this claim with an argument by cases according to the truth value of P.
Transcribed Image Text:C(2) a2n+1 Tn P2n+1 an+2 an+1 (n+1)-bit add1 C(1) ri To 2(n+2)-bit addl module Figure 3.1 Pn+2 Pn+1 an Pn a₁ ao (n+1)-bit add1 Structure of a Double-size add1 Module. PI Po (b) Instead of a truth-table, prove this claim with an argument by cases according to the truth value of P.
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