Mathematical ReasoningHard
Question
The statement p → (q → p) is equivalent to
Options
A.p → (p → q)
B.p → (p ∨ q)
C.p → (p ∧ q)
D.p → (p ↔ q)
Solution
p → (q → p) = ~ p ∨ (q → p)
= ~ p ∨ (~q ∨ p) since p ∨ ~ p is always true
= ~ p ∨ p ∨ q = p → (p ∨ q).
= ~ p ∨ (~q ∨ p) since p ∨ ~ p is always true
= ~ p ∨ p ∨ q = p → (p ∨ q).
Create a free account to view solution
View Solution FreeMore Mathematical Reasoning Questions
If C and D are two events such that and P(D) ≠ 0, then the correct statement among the following is...A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30...In an LCR circuit as shown below both switches are open initially. Now switch S1 is closed, S2 kept open, (q is charge o...The anode voltage of photocell is kept fixed. The wavelength λ of the light falling on the cathode is gradually cha...In a certain town, 25% of the families own a phone and 15% own a car; 65% families own neither a phone nor a car and 2,0...