tut06.pdf - Mat1101 Tutorial Week 6 Logic Grossman Chapter...

Mat1101 Tutorial Week 6
Logic
Grossman Chapter 4
1. Construct truth tables to verify the following laws.
(a) ¬(? ∨ ?) ≡ ¬? ∧ ¬? (de Morgan's second law)
(b) ? → ? ≡ ¬? ∨ ? (implication law)
(c) ? ∧ (? ∨ ?) ≡ ? (first absorption)
2. Consider the following two propositions:
? ≡ It is snowing ? ≡ I go skiing .
(a) Write the implication ? → ? in plain english.
(b) Write the inverse, the converse and the contrapositive of
this implication using the logical symbols ∧, ∨, ¬, or → as
required.
(c) Construct truth tables of the implication, and it's inverse,
converse, and contrapositive. Hence, determine which are
logically equivalent.
(d) Write the inverse, the converse and the contrapositive of
this implication in plain English.
3. Consider the following proposition.
¬(? ∨ ¬?) ∨ ?.
(a) Construct a truth table for the proposition above.
(b) Construct a truth table for ? ∨ ? . Compare this truth table
with one constructed in the previous part. What can you