Show, 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.

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. 

The negation of  is equivalent to

The statement ~ (p↔ ~q) is 

• equivalent to p ↔ q

• equivalent to ~ p ↔q

• a tautology

• a tautology

The variance of first 50 even natural number is

• 833/4

• 833

• 437

• 437

98.

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