¬ ↔ ≡ ↔¬ . Check whether the statement p ® ® ) is a tautology or a contradiction without using the truth table. . Using truth table check whether the statements ¬ ∨¬ ∧ q and ¬ p are logically equivalent.
. Prove p ) ≡ without using truth table. . Prove that p →¬ ∨ ¬ ∨¬ ∨ ≡ ) using truth table.
EXERCISE . Choose the correct or the most suitable answer from the given four alternatives. . A binary operation on a set S is a function from ( ) S S ® ( ) S S S × ) → ( ) S S S × ( ) S S S S × ) → × .
Subtraction is not a binary operation in ( ) ( ) ( ) ( ) . Which one of the following is a binary operation on ? ( ) Subtraction ( ) Multiplication ( ) Division ( ) All the above . In the set of real numbers ‘ * ’ is defined as follows.
Which one of the following is not a binary operation on ? ( ) a b ∗= min ( a b × ( ) a b ∗= max ( , ) a b ( ) a b ∗= ( ) a b a b ∗= . The operation * defined by a b ab ∗= is not a binary operation on ( ) + ( ) ( ) ( ) . In the set define a ab + + .
For what value of y, ) = ? ( ) y = ( ) y = − ( ) y = − ( ) y = . If a b ∗= on the real numbers then * is ( ) commutative but not associative ( ) associative but not commutative ( ) both commutative and associative ( ) neither commutative nor associative - - . Which one of the following statements has the truth value T ?
( ) sin x is an even function. ( ) Every square matrix is non-singular ( ) The product