Practice Questions 5 – Mathematical Reasoning – Class XI

Find the contrapositive of the statement “If Smita is intelligent, then she will join Medical” is

Find the inverse of the statement “If Smita is intelligent, then she will join Medical” is

Find the converse of the statement “If Smita is intelligent, then she will join Medical” is

“Either the girls are happy or they are not playing.” Express it in prepositional logic.

“Girls are unhappy but they are playing.” Express it in prepositional logic.

“It is not true that the girls are not playing but they are happy.” Express it in prepositional logic.

If p and q are true and s is false then \( (p \cap q) \cup s \) is

Find the truth value of \( \left[ {\left( {p \to q} \right) \cap q} \right] \to p\)

\(\left( {p \cap q} \right) \to r\) is equivalence to

\(\left[ {\left( {p \cup q} \right) \cap \sim p} \right] \cap \left( {\sim q} \right)\) is equivalence to

If \( \phi = \left[ {\left( {p \cap q} \right) \to \left( {\sim p \cup \sim q} \right)} \right] \cap \sim p\) then the truth value of \( \phi \) is

Find the truth value of \( \left[ {p \cap \left( {p \to q} \right)} \right] \to q\)

\(\left( {p \cap q} \right) \cup \left( {\sim p \cap q} \right) \cup \left( {p \cap \sim q} \right) \cup \left( {\sim p \cap \sim q} \right)\)

Find the converse of the statement ” If an angle is a right angle, then its measure is \(90^\circ \)

Find the inverse of the statement ” If an angle is a right angle, then its measure is \(90^\circ \)

Find the conrapositive of the statement ” If an angle is a right angle, then its measure is \(90^\circ \)

The preposition \( p \cap \sim p \) is

The preposition \( q \cup \sim q \) is

When two statements are corrected by the connective “if and only if” then the compound statement is called

If p and q be two statements then the conjuction of the statements, \( p \cap q \) is true when