Mathematics for Computer Science

“mcs” — 2017/3/3 — 11:21 — page 76 — #84
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Chapter 3
Logical Formulas
M IMPLIES Q
M IMPLIES .P OR Q/
M IMPLIES ŒM AND .P IMPLIES M /
.P OR Q/ IMPLIES Q
.P OR Q/ IMPLIES .P AND Q/
.P OR Q/ IMPLIES ŒM AND .P IMPLIES M /
.P XOR Q/ IMPLIES Q
.P XOR Q/ IMPLIES .P OR Q/
.P XOR Q/ IMPLIES ŒM AND .P IMPLIES M /
Problem 3.11.
Show truth tables that verify the equivalence of the following two propositional
formulas
.P XOR Q/;
NOT.P IFF Q/:
Problem 3.12.
Prove that the propositional formulas
and
P OR Q OR R
.P AND NOT.Q// OR .Q AND NOT.R// OR .R AND NOT.P // OR .P AND Q AND R/:
are equivalent.
Problem 3.13.
Prove by truth table that OR distributes over AND, namely,
P OR .Q AND R/ is equivalent to .P OR Q/ AND .P OR R/ (3.29)