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Show that [(ptoq)^^(qto r)] to ( p to r)...

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

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Truth values of `[(p to q) ^^(q to r)] to (p to r) `

For all possible truth values of p and q , the compound statement `[(p to q)^^(q to r)] to (p to r) ` is true.
Thus, `[(p to q) ^^(q to r) ] to ( p to r)` is a tautolgy.
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Knowledge Check

  • consider : Statement - I : (p^^~q)^^(~p^^q) is a fallacy . Statement -II : (prarrq)harr(~qrarr~p) is a tautology .

    A
    Statement -I is true , Statement -II is true , Statement -II is a correct explantion for Statement - I .
    B
    Statement - I is true , Statement - II is true , Statement -II is not a correct explanation for Statement -I .
    C
    Statement - I is true , Statement -II is false .
    D
    Statement - I is false , Statement -II is true .

  • Statement I : (p^^∼q)∧(∼p^^q) is a fallacy. Statement II : (p→q)↔(∼q→∼p) is a tautology.

    A
    Statement 1 is true, Statement-2 is true.
    Statement-2 ia not a correct explation for Statement-1
    B
    Statement-1 is true, Statement-2 is false
    C
    Statement-1 is false, Statement-2 is true
    D
    Statement-1 is true, Statement-2 is true, Statement-2 is a correct explanation for Statement-1

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