Question
Asked Oct 25, 2019

 Discrete Structures

Section 1.2

Exercise

Q9 and Q11. Show that each of the following conditional statements is a tautology using truth tables and without using truth tables.

 

а) (рла) — р
с) -р — (р—9)
e) - (р — 9) —р
b) р — (рVq)
d) (рла) — (р— 9)
f) - (р — 9) —
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а) (рла) — р с) -р — (р—9) e) - (р — 9) —р b) р — (рVq) d) (рла) — (р— 9) f) - (р — 9) —

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check_circleExpert Solution
Step 1
    • With using Truth Table:
    • a. ( p ^ q ) -> p

p

q

p^q

(p^q) -> p

0

0

0

1

0

1

0

1

1

0

0

1

1

1

1

1

 

 

  • b. p -> ( p v q )

p

q

p^q

(p^q) -> p

0

0

0

1

0

1

0

1

1

0

0

1

1

1

1

1

p

q

pvq

p -> (pvq)

0

0

0

1

0

1

1

1

1

0

1

1

1

1

1

1

 

  • c. NOT( p ) -> ( p -> q )

p

q

NOT(p)

p -> q

NOT(p) -> (p->q)

0

0

1

1

1

0

1

1

1

1

1

0

0

0

1

1

1

0

1

1

Hence, proved that a, b, c statements is a tautology  

...

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