Mathematical ReasoningHard
Question
Consider the following statements :
P : Suman is brilliant
Q : Suman is rich.
R : Suman is honest
the negation of the statement
″Suman is brilliant and dishonest if and only if suman is rich″ can be equivalently expressed as :
P : Suman is brilliant
Q : Suman is rich.
R : Suman is honest
the negation of the statement
″Suman is brilliant and dishonest if and only if suman is rich″ can be equivalently expressed as :
Options
A.~ Q ↔ ~ P ∨ R
B.~ Q ↔ ~ P ∧ R
C.~ Q ↔ P ∨ ~ R
D.~ Q ↔ P ∧ ~ R
Solution
Given statement is equal to (p ∧ ~ R) ↔ Q
Negation of the above statment is ~ Q ↔ (p ∧ ~R)
~ Q ↔ P ∧ ~ R
Negation of the above statment is ~ Q ↔ (p ∧ ~R)
~ Q ↔ P ∧ ~ R
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