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JEE Maths Quiz on Mathematical Reasoning
JEE Maths Quiz on Mathematical Reasoning : In this article you will get to Online test for JEE Main, JEE Advanced, UPSEE, WBJEE and other engineering entrance examinations that will help the students in their preparation. These tests are free of cost and will useful in performance and inculcating knowledge. In this post we are providing you quiz on Mathematical Reasoning
Quiz on Mathematical Reasoning
Q1. Which of the following is the contrapositive of if two triangles are identical, then these are similar?
a) if two triangles are not similar, they are not identical
b) If two triangles are not identical, then these are not similar
c) If two triangles are not identical, then these are similar
d) If two triangles are not similar, then these are identical
a) if two triangles are not similar, they are not identical
Solution:
Consider the following statements
p: Two triangles are identical.
q: Two triangles are similar.
Clearly, the given statement in symbolic form is p ⇒ q.
Therefore, its contrapositive is given by ∼ q ⇒ ∼ p
Now,
∼p: two triangles are not identical.
∼q: two triangles are not similar.
Therefore, ~ q ⇒ ~ p: If two triangles are not similar, then these are not identical.
Q2. If p is true and q is false, then which of the following statements is not true?
a) p ∨ q
b) p ⇒ q
c) p ∧ ( ~q)
d) q ⇒ p
b) p ⇒ q
Q3. Which of the following is logically equivalent to ~( ~ p ⇒ q)?
a) p ∧ q
b) p ∧ ~q
c) ~p ∧ q
d) ~p ∧ ~q
d) ~p ∧ ~q
Q4. The Boolean Expression (p ∧ ~q) ∨ q ∨( ~p ∧ q) is equivalent to ___________.
a) p ∨ q
b) p ∧ q
c) ~p ∧ q
d) ~p ∧ ~q
a) p ∨ q
Solution:
[(p ∧ ∼q) ∨ q] ∨ (∼p ∧ q) = (p ∨ q) ∧ (∼q ∨ q) ∨ (∼p ∧ q)
= (p ∨ q) ∧ [t ∨ (∼p ∧ q)]
= (p ∨ q) ∧ t
= p ∨ q
Q5. If each of the following statements is true, then P ⇒ ~q, q ⇒ r, ~r
a) p is false
b) p is true
c) q is true
d) None of these
a) p is false
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