Reasoning QUIZ-13

Mathematical Reasoning Quiz-13

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 .

Q1. ~(~p→q)≡

•  p∧~q
•  ~p∧q
•  ~p∧~q
•  ~p∨~q

Solution
(c) ∼(∼p⟶q)≡∼p∧∼q

Q2.Logical equivalent proposition to the proposition ~(p∨q)

•  ∼p∧∼q
•  ∼p∨∼q
•  ∼p→∼q
•  ~p ↔ ~q

Solution
(a) By De’Morgan’s law, we have p∨q=∼p∧∼q

Q3.  Which of the following is not a proposition?

•  
  
•  
  
•  Mathematics is interesting
•  5 is an even integer

Solution
(c) Mathematics is interesting is not a logical sentence. It may be intersecting for some persons and may not be interesting for others ∴ This is not a proposition

Q4. Identify the false statement

•  [~p∨~q]≡(~p)∧q
•  [p∨q]∨(~p) is a tautology
•  [p∧q]∧(~p) is a contradiction
•  ~(p∨q)=p∨(~q)

Solution
(d)

Q5.Which of the following is contingency?

•  p∨∼p
•  p∧q ⇒ p∨q
•  p∧∼q
•  None of these

Solution
 (c)

Q6. The dual of the statement [p∨~q]∧(~p) is

•  p∨(~q)∨~p
•  (p∧~q)∨~p
• p∧~(q∨~p)
•  None of these

Solution
(b) The dual of the given statement is (𝑝∧~𝑞)∨~𝑝.

Q7.Which of the following pairs are logically equivalent?

•  Conditional, Contrapositive
•  Conditional, Inverse
•  Contrapositive, Converse
•  Inverse, Contrapositive

Solution
(a)

Q8.The negation of the statement "he is rich and happy" is given by

•  he is not rich and not happy
•  he is not rich or not happy
•  he is rich and happy
•  he is not rich and happy

Solution
(b) The negation of the given statement is “he is not rich or not happy”.

Q9.The contrapositive of (∼p∧q)→~r is

•  (p∧q)→r
•  (p∨q)→r
•  r→(p ∨∼q)
•  None of these

Solution
(c) We know that the contrapositive of 𝑝→𝑞 is ∼𝑞→∼𝑝. Therefore, contrapositive of (∼𝑝∧𝑞)→∼𝑟 is 𝑟→∼(∼𝑝∧𝑞) or, 𝑟→𝑝∨∼𝑞

Q10. If p,q,and r are simple propositions with truth values T,F,T, then the truth value of ~p∨q∧∧~q→p is

•  True
•  False
•  True, if r is false
• None of these

Solution
(a)