Home
Class 12
MATHS
Determine whether each of the following ...

Determine whether each of the following statement patterns is a tautology or a contradiction or contingency :
(1) `[(ptoq)^^~q]to(~p)`
(2) `(p^^~q)iff(ptoq)`
(3) `(p^^q)vv(p^^r)`

Text Solution

Verified by Experts


All the entries in the last column of the above truth table are T.
`:. [(p to q) wedge ~q] to ( ~p)` is a tautology.

All the entries in the last column of the above truth table are F.
`:.(p^^~q)iff(ptoq)` is a contradiction.

The entries in the last column of the abvoe truth table are neither all T nor all F.
`:.(p^^q)vv(p^^r)` is a contingency.
Promotional Banner

Topper's Solved these Questions

  • MATHEMATICAL LOGIC

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise EXAMPLES FOR PRACTICE 2 OR 3 MARKS EACH|24 Videos

  • MATHEMATICAL LOGIC

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise EXAMPLES FOR PRACTICE 3 MARKS EACH|4 Videos

  • LINEAR PROGRAMMING

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise EXAMPLES FOR PRACTICE|8 Videos

  • MATRICES

    NAVNEET PUBLICATION - MAHARASHTRA BOARD|Exercise MULTIPLE CHOICE QUESTIONS|12 Videos

Similar Questions

Explore conceptually related problems

Examine whether the following logical statement pattern is tautology, contradication or contingency. [(pto q) ^^q] to p

Using truth tables, determine wether the following statements are tautology or contradiction or contingency : (1) ~(~p^^~q)vvq (2) [(pvvq)^^~p]^^(~q)

Answer the following questions Examine whether the statement pattern is a tautology, contradiction or contingency (p ^^ ~q) rarr (~p ^^ ~q)

Using truth tables. Examine whether the stateements pattern (p^^q) v(p^^r) is tautology. Contradiction or continegency.

Which of the following statement is acontradiction (p^^q)^^(sim(p vv q))

Verify that the statement P vee ~( p ^^ q) is a tautology.

The statement p vv q is

~[(p ^^ q)to(~p vv q)] is a

Which of the following statement is a contradiction: (1)(sim p vv sim q)vv(p vv sim q),(2)(p rarr q)vv(p^^sim q),(3)(sim p^^q)^^(sim q)