Assertion & reason in Mathematics

1.Statement I : gof : A → C is one one
Statement II - gof : A → C is onto

2. let A nd B be two events such that P(A ∩ B) =1/4 and P(A)=1/2 and P(B)= 1/2 then
A- A and B are independent events
R- P(A ∩ B) ≠P(A).P(B)

3. Let a * b =(a+b)/2
A- * is commulative but not associative
R- * is a binary operation

4. A- Let vectors 4a+5b+c, -b-c and 5a+9b+4c are coplanar, where vectors a,b,c are non-coplanar
R- If p= λ(q x r) then p,q,r are non- coplanar

5- A- Rolle's Theorem apply for f(x)= x^2+2x-8 on [-4,2]
R- f '(x) exists on [–4, 2]

6. A- For the function f(x)= 4x^3+9x^2-12x has local maxima at x = –2
R- f '(–2) = 0 and f ' (–2) > 0

7. A- If A = {1, 2, 3} and R = {(1, 1), (2, 2), (1, 2) (2, 1)} then R is reflexive relation.
R- The relation R is symmetric and transitive.

8. A- Let f : N → Y be a function defined 7. as f(x) = 9x + 3 where Y = {y : y = 9x + 3, x belongs to N}, then f is one-one
R- For x1, x2 belongs to N we have f(x1) = f(x2) i.e, x1 = x2

9. A- Let R be a relation over set A = {1, 2, 3} defined as R={(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)} then R is an equivalence relation
R- R is reflexive, symmetric and transitive

10. A- If A be the set of all lines in the plane then the relation parallel is an equivalence relation
R- If A be the set of all lines in the plane then the relation parallel is an equivalence relation

11. A- Let A = R – {3} and B = R – {1}. Consider the function f : A →B defined by f(x ) =
(x-2)/(x-3) then f(x) is one one
R- f(x) is onto