MATHEMATICS REASONING QUIZ-7
Dear Readers,
As per analysis for previous years, it has been observed that students preparing for JEE MAINS find Mathematics out of all the sections to be complex to handle and the majority of them are not able to comprehend the reason behind it. This problem arises especially because these aspirants appearing for the examination are more inclined to have a keen interest in Mathematics due to their ENGINEERING background.
Furthermore, sections such as Mathematics are dominantly based on theories, laws, numerical in comparison to a section of Engineering which is more of fact-based, Physics, and includes substantial explanations. By using the table given below, you easily and directly access to the topics and respective links of MCQs. Moreover, to make learning smooth and efficient, all the questions come with their supportive solutions to make utilization of time even more productive. Students will be covered for all their studies as the topics are available from basics to even the most advanced.
Q2.The proposition (p→~p)∧(∼p→p) is a
:
Solution
We have, p→∼p≅∼p∨∼p≅∼p and ∼p→p≅p∨p≅p ∴(p→∼p)∧(∼p→p)≅∼p∧p≅c
We have, p→∼p≅∼p∨∼p≅∼p and ∼p→p≅p∨p≅p ∴(p→∼p)∧(∼p→p)≅∼p∧p≅c
Q4. The contrapositive of (p∨q)→r is
Solution
Contrapositive of (p∨q)→r is ∼r→∼(p∨q)≡∼r→(∼p∧∼q)
Contrapositive of (p∨q)→r is ∼r→∼(p∨q)≡∼r→(∼p∧∼q)
Q5.p→q is logically equivalent to
Solution
We have p→q≅∼p∨q and,∼q→∼p≅∼(∼q)∨∼p≅q∨∼p≅∼p∨q≅p→q
We have p→q≅∼p∨q and,∼q→∼p≅∼(∼q)∨∼p≅q∨∼p≅∼p∨q≅p→q
Q6. Let p be the proposition Mathematics is interesting and let q be the proposition that Mathematics is difficult, then the symbol p∧q means
Solution
p∧q means Mathematics is interesting and Mathematics is difficult
p∧q means Mathematics is interesting and Mathematics is difficult
Q7.∼[∼p∧(p⇔q)]≡
Q10. Which of the following not a statement in logic?
1. Earth is planet.
2. Plants are living objects.
3. √(-3)is a rational number.
4. x2-5x+6<0 when x∈-R
Solution
Plants are living objects is not a statement.
Plants are living objects is not a statement.