Short Answer TypeShow, by method of contrapositive, that following statement is true.
“If x is an integer and x2 is odd, then x is also odd
Show that the statement
p: “If x is a real number such that x3 + 4x = 0, then x is 0” is true by direct method.
Show that the statement
p: “If x is a real number such that x3 + 4x = 0, then x is 0” is true by method of contradiction.
The component statements of the given statement are
q : x is a real number such that x3 + 4x = 0
r : x is 0.
In this method, we assume p is not true.
i.e, If x is a real number such that 
then 
i.e., 
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i.e, 
which is not possible as x is a real number.
Therefore, our supposition is wrong.
Hence, p is true.
Show that the statement
p: “If x is a real number such that x3 + 4x = 0, then x is 0” is true by method of contrapositive.
Multiple Choice QuestionsThe statement ~ (p↔ ~q) is
equivalent to p ↔ q
equivalent to ~ p ↔q
a tautology
a tautology
Consider :
Statement − I : (p ∧ ~ q) ∧ (~ p ∧ q) is a fallacy.
Statement − II : (p → q) ↔ (~ q → ~ p) is a tautology.
Statement -I is True; Statement -II is True; Statement-II is a correct explanation for Statement-I
Statement - I is True; Statement -II is true; Statement-II is not a correct explanation for Statement-I
Statement -I is True; Statement -II is False.
Statement -I is True; Statement -II is False.
The negation of the statement “If I become a teacher, then I will open a school” is
I will become a teacher and I will not open a school
Either I will not become a teacher or I will not open a school
Neither I will become a teacher nor I will open a school
Neither I will become a teacher nor I will open a school
Consider the following statements
P: Suman is brilliant
Q: Suman is rich
R: Suman is honest. The negation of the statement ì Suman is brilliant and dishonest if and only if Suman is richî can be ex- pressed as
~ P ^ (Q ↔ ~ R)
~ (Q ↔ (P ^ ~R)
~ Q ↔ ~ P ^ R
~ Q ↔ ~ P ^ R
Switch
is equivalent to
