Home
Class 12
MATHS
Show that [(ptoq)^^(qto r)] to ( p to r)...

Show that `[(ptoq)^^(qto r)] to ( p to r)`is a tautology

Text Solution

AI Generated Solution

To show that the expression \([(p \to q) \land (q \to r)] \to (p \to r)\) is a tautology, we will construct a truth table and analyze the values step by step. ### Step 1: Define the Variables We have three variables: \(p\), \(q\), and \(r\). Each variable can either be true (T) or false (F). ### Step 2: Create the Truth Table Since there are three variables, we will have \(2^3 = 8\) possible combinations of truth values for \(p\), \(q\), and \(r\). ...
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

Show that (pvvq) to r -= (p to r) ^^ (q to r)

Show that [(pvvq)vvr] harr [pvv(qvvr)] is a tautology

Show that (i) ~ [ p ^^ ( ~p) ] is a tautology (ii) ~ [ p vee ( ~ p)] is a contradication.

Show that (i) p to (pvvq) is a tautology (ii) (pvvq) ^^(~ p ^^~q) is a contradiction

Using truth table , prove that : (ptoq)to[(~ptoq)toq] is a tautology.

Consider : Statement I: (p^^~q)^^(~p^^q) is a fallacy Statement II: (ptoq)harr(~q to ~p) is a tautology

For any statements p, show that . (i) p vee ~ p is a tautology , ( ii) p ^^ ~ p is a contradiction

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

Which of the following is false? a. (p=>q)hArr(~ q=>~ p) is a contradiction b. pvv(~ p) is a tautology c. ~(~ p)hArr(~ q=>~ p) is a tautology d. p^^(~ p) is a contradiction

Prove by construction of truth table that p vv ~ (p ^^q) is a tautology