Home
Class 12
MATHS
Show that ~(p harr q) -= ( p ^^ ~q) vv(~...

Show that `~(p harr q) -= ( p ^^ ~q) vv(~p ^^q)`.

Text Solution

AI Generated Solution

To show that \( \neg (p \harr q) \equiv (p \land \neg q) \lor (\neg p \land q) \), we will use a truth table to evaluate both sides of the equivalence. ### Step 1: Construct the Truth Table We need to evaluate the expressions for all possible truth values of \( p \) and \( q \). The possible combinations of truth values for \( p \) and \( q \) are: - \( T, T \) - \( T, F \) ...
Promotional Banner

Topper's Solved these Questions

  • MATHMETICAL REASONING

    CENGAGE ENGLISH|Exercise Single correct answer type|38 Videos
  • MATHMETICAL REASONING

    CENGAGE ENGLISH|Exercise Archives|10 Videos
  • MATHMETICAL REASONING

    CENGAGE ENGLISH|Exercise Archives|10 Videos
  • LOGARITHM AND ITS PROPERTIES

    CENGAGE ENGLISH|Exercise JEE ADVANCED|1 Videos
  • MATRICES

    CENGAGE ENGLISH|Exercise Single correct Answer|34 Videos

Similar Questions

Explore conceptually related problems

(p^^~q)^^(~p^^q) is

(p^^~q)^^(~p^^q) is

(p ^^ ~q) ^^ (~p vv q) is

Match the following column s: Column-I " " Column-II Negation of (~ p->q) is " " p. [~(p v q)]^^[p v(~ p)] Negation of (pharrq) " " q. (p^^~ q)vv(~ p^^q) Negation of (pvvq)i s " " r. ~ p^^~ q pharrq is equivalent to " " s. ~ p^^~ q

Show that ( p vee q) ^^ ( ~ p ^^ ~ q) is a contradion .

Using truth table show that - (p vv q) vv (~ p ^^ q ) is logically equivalent to ~ p.

The negation of (~p ^^ q) vv (p ^^ ~ q) is

The statement ~(p ^^ q) vv q

Observe the following statements I : The dual of [ ~p ^^ q)] vv [ p ^^ {~(q vv ~s)}] is [~(p vv q)] ^^ [p vv{~(q ^^ ~s)}] II : The dual of ~p ^^ [(~q) ^^ (p vv q) ^^ ~r] is ~p vv[~q) vv(p ^^ q) vv ~r] The true statements in the above is/are :

p^^(~p vv~q)^^q-= ?