, By O.P. GUPTA
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M.+919650350480
In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R).
Choose the correct answer out of the following choices.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true and R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true.
Q01. Assertion (A) : The relation R {(a, b) : a b 2} on the set R of real nos. is not reflexive.
Reason (R) : A relation on a set A is reflexive if (a, a) R a A .
Q07. Assertion (A) : Let f : R R defined as f (x) x , here . represents the greatest integer
function. Then f is not one-one.
Reason (R) : A function is one-one if f () f () implies .
Q11. Assertion (A) : Number of all onto functions from the set {1, 2, 3, 4} to itself is 24.
Reason (R) : Onto functions from the set {1, 2, 3, …, n} to itself is simply a permutation on n
symbols namely 1, 2, 3, …, n.
Q27. Assertion (A) : Inverse of sin x does not exist in x R .
Reason (R) : All trigonometric functions are many-one in their respective domain.
Q30. Assertion (A) : A function f shown below by the arrow diagram, is one-one.
Reason (R) : A function f : A B is one-one if f (α) f (β) implies α β for all α, β A .
Q38. X {0, 2, 4, 6, 8}.
P is a relation on X defined by P {(0, 2), (4, 2), (4, 6), (8, 6), (2, 4), (0, 4)}.
Assertion (A) : The relation P on set X is a transitive relation.
Reason (R) : The relation P has a subset of the form {(a , b), (b, c), (a , c)}, where a , b, c X.
492 MATHEMATICIA By O.P. GUPTA : A New Approach in Mathematics
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