Proposition Al Equivalence S
Proposition Al Equivalence S
Proposition Al Equivalence S
T T
T F
F T
F F
Solution
T T F
T F F
F T T
F F T
Solution
T T F T
T F F T
F T T T
F F T F
Solution
p q ¬p p q ¬p (p q ) [¬p (p q )]q
T T F T F
T F F T F
F T T T T
F F T F F
Solution
T T F T F T
T F F T F T
F T T T T T
F F T F F T
Since the truth table shows all the true values of compound proposition
[¬p (p q )]q are true(T), so it is a tautology.
Class Work
Since the truth values of both of the compound propositions are same in the
corresponding rows, they are logically equivalent.
Class Work
Since the truth values of both of the compound propositions are same in the
corresponding rows, they are logically equivalent.
Logical Equivalences
Table 6 ( page 24 ) Rosen, 7th edition
A very Useful Logical Equivalence(ULE)
pq¬pq
Example 1
Show that ¬(p q) and p ¬ q are logically equivalent.
Solution:
by ULE
Example 7 (page 26)
Solution:
Exercise