Discrete Math Prove or Disprove Discrete Math Prove or Dispr

Discrete Math

Prove or Disprove

Discrete Math Prove or Disprove (A intersection B) = (A union B) reversible A= B (V union W)^c = V^c intersection W^c C subset D? reversible C intersection D = C X union phi = X

Solution

Ans 4) Suppose X={1,2,3} and contains null i.e the set of the symbol contains null value.

So, X = X will result in the same set that is X.

Ans 2) Suppose ,

Let P = (V U W)\' and Q = V\' W\'

Let x be an arbitrary element of P then x P x (V U W)\'

x (V U W)

x V and x W

x V\' and x W\'

x V\' W\'

x Q

Therefore, P Q …………….. (i)

Again, let y be an arbitrary element of Q then y Q y V\' W\'

y V\' and y W\'

y V and y W

y (V U W)

y (V U W)\'

y P

Therefore, Q P …………….. (ii)

Now combine (i) and (ii) we get; P = Q i.e. (V U W)\' = V\' W\'

Answer 1 and 3 is not known to me.

Hence can\'t write the proofs.