Home
Class 12
MATHS
Show that (pvvq) to r -= (p to r) ^^ (q ...

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

Text Solution

AI Generated Solution

To show that \((p \lor q) \to r = (p \to r) \land (q \to r)\), we will analyze both sides of the equation step by step. ### Step 1: Understand the expressions We need to evaluate both sides of the equation: - Left-hand side (LHS): \((p \lor q) \to r\) - Right-hand side (RHS): \((p \to r) \land (q \to r)\) ### Step 2: Construct a truth table ...
Promotional Banner

Topper's Solved these Questions

  • MATHMETICAL REASONING

    CENGAGE ENGLISH|Exercise concept application|13 Videos
  • MATHMETICAL REASONING

    CENGAGE ENGLISH|Exercise Single correct answer type|38 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 (i) p to (pvvq) is a tautology (ii) (pvvq) ^^(~ p ^^~q) is a contradiction

If q is the mean proportional between p and r , show that : pqr (p + q + r)^(3) = (pq + qr + pr)^(3) .

Construct the truth table for the followings statements : (a) (p^^q) to ~ p " " (b) (p^^q) to (pvvq) (c) (p^^q) to r " " (d) [p^^(~r)] to (qvvr)

If p^(th) term of an A.P. is q and its q^(th) term is p, show that its r^(th) term is (p + q - r)

(a) If r^(2) = pq , show that p : q is the duplicate ratio of (p + r) : (q + r) . (b) If (p - x) : (q - x) be the duplicate ratio of p : q then show that : (1)/(p) + (1)/(q) = (1)/(r) .

The contrapositive of (pvvq) to r is

In Figure, P Q R S is a quadrilateral in which diagonals P R\ a n d\ Q S intersect in O . Show that : (i) P Q+Q R+R S+S P > P R+Q S (ii) P Q+Q R+R S+S P<2(P R+Q S)

If pth, qth , rth and sth terms of an AP are in GP then show that (p-q), (q-r), (r-s) are also in GP

P and Q are any two points lying on the sides DC and AD respectively of a parallelogram ABCD . Show that a r\ (A P B)\ =\ a r\ (B Q C) .

The logical statement [~(~pvvq)vv(p^^r)]^^(~q^^r) is equivalent to (a) (~p^^~q)^^r (b) ~p vv r (c) (p^^r)^^~q (d) (p^^~q)vvr