REASONING-QUIZ-4

MATHEMATICS REASONING QUIZ-4

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. The statement (p⇒q)⇔(∼p∧q) is a

•  Tautology
•  Contradiction
•  Neither (a) nor (b)
•  None of these

Q2.Which of the following is logically equivalent to (p∧q)? :

•  p→q
•  ∼p∧∼q
•  p∧∼q
•  ∼(p→∼q)

Solution
We have, ∼(p→∼q)≅∼(∼p∨∼q)≅p∧q

Q3.  All teachers are scholar, Identify the Venn diagram

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Solution

Q4. If p always speaks against q, then p⇒p∨∼q is

•  A tautology
•  Contradiction
•  Contingency
•  None of these

Q5.Consider the proposition : “If we control population growth, we prosper”. Negative of this proposition is

•  If we do not control population growth, we prosper
•  If we control population, we do not prosper
•  We control population but we do not prosper
•  We do not control population but we prosper

Solution
 Consider the following statements: p∶ We control the population growth q∶ We become prosper The given statement is p→q and its negation is p∧∼q i.e. We control population but we donot become prosper

Q6. If p and q are statements, then ∼(p∧q)∨∼(q⇔p) is

•  Tautology
•  Contradiction
•  Neither tautology nor contradiction
•  Either tautology or contradiction

Solution

Q7.If p and q are two statements, then (p⇒q)⇔(∼q⇒~p) is a

•  Contradiction
•  Tautology
•  Neither (a) nor (b)
•  None of these

Solution

Q8.Negation of the conditional, "If it rains, I shall go to school" is

•  It rains and I shall go to school
•  It rains and I shall not go to school
•  It does not rains and I shall go to school
•  None of the above

Solution
Let p: It rains, q: I shall go to school Thus, we have p→q Its negation is ∼(p→q)ie,p∧∼q ie,It rains and I shall not go to school.

Q9.Simplify the following circuit and find the boolean polynomial.

•  p∨(q∧r)
•  p∧(q∨r)
•  p∨(q∨r)
•  p∧(q∧r)

Solution
(p∨q)∧(p∨r)=p∨(q∧r)

Q10. The negation of p∧(q→~r) is

•  ~p∧(q∧r)
•  p∨(q∨r)
•  p∨(q∧r)
•  ~p∨(q∧r)

Solution
∼(p∧(q⟶∼r) )=∼p∨∼(q⟶∼r) =∼p∨(q∧∼(∼r)) =∼p∨(q∧r)