Advertisement Remove all ads

Without using truth table, show that (p ∨ q) → r ≡ (p → r) ∧ (q → r) - Mathematics and Statistics

Sum

Without using truth table, show that

(p ∨ q) → r ≡ (p → r) ∧ (q → r)

Advertisement Remove all ads

Solution

L.H.S.

≡ (p ∨ q) → r

≡ ~ (p ∨ q) ∨ r          ....[p → q → ~ p ∨ q]

≡ (~ p ∧ ~ q) ∨ r       ....[De Morgan’s law] 

≡ (~ p ∨ r) ∧ (~ q ∨ r)       .....[Distributive law]

≡ (p → r) ∧ (q → r)             .....[p → q → ~ p ∨ q]

= R.H.S.

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×