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
Let A = . The only correct statement about the matrix A is...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...If C and D are two events such that and P(D) ≠ 0, then the correct statement among the following is...The statement ~ (p ↔ ~ q) is...The negation of the statement″If I become a teacher, then I will open aschool″, is :...