REASONING-QUIZ-9

MATHEMATICS REASONING QUIZ-9

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. If p= He is intelligent q=He is strong Then, symbolic form of statement "It is wrong that he is intelligent or strong," is

•  ∼p∨∼p
•  ∼(p∧q)
•  ∼(p∨q)
•  p∨∼q

Solution
The symbolic form of given statement is ∼(p∨q)

Q2. Which of the following is false?

•  p∨∼p is a tautology
•  ∼(∼)↔p is a tautology
•  (p∧(p→))→ is a contradiction
•  p∧∼p is a contradiction

Solution
Clearly, p∨∼pis always true. So, it is a tautology We have, ∼(∼p)↔p≅p↔p So, ∼(∼p)↔p is always true. So, it is a tautology We know that p→q≅∼p∨q ∴p∧(p→q)≅p∧(∼p∨q)≅(p∧∼p)∨(p∧q) ≅c∨(p∧q)≅p∧q ∴p∧(p→q)→p≅p∧q→p which is a tautology So, option (c) is false

Q3.  (p∧~q)∧(~p∧q) is

•  a tautology
•  a contradiction
•  tautology and contradiction
•  neither a tautology not a contradiction

Solution

Q4. Which of the following is logically equivalent to ∼(p↔q)?

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

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

Q5.If p→(q∨r) is false, then the truth values of p,q,r are respectively

•  F, T, T
•  T, T, F
•  T, F, F
•  F, F, F

Q6. The logically equivalent proposition of p→q is

•  (p→q)∨(q→p)
•  (p∨q)→(p∨q)
•  (p∧q)∧(p∨q)
•  (p→q)∧(q→p)

Q7.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≅∼p∨∼q≅∼(p∧q) So, option (a) is not correct ∼p∨∼q=∼(p∧q) So, option (b) is not correct ∼(p→∼q)=∼(∼p∨∼q)=p∧q So, option (c) is incorrect

Q8.Dual of (x^'∧y^' )^'=x∨y is
ax+by+bz=0
bx+ay+bz=0
bx+by+az=0
Will have a non-trivial solution, is

•  (x^'∧y^' )=x∧y
•  (x^'∨y^' )^'=x∧y
•  (x^'∨y^' )^'=xy
•  None of these

Q9.If p and q are two statements, then statement p⇒q∧∼q is

•  Tautology
•  Contradiction
•  Neither tautology not contradiction
•  None of the above

Solution

Q10. The switching function for switching work is

•  x∧y∧z
•  x∨y∧x∨z
•  x∧y∧x∨z
•  None of these

Written by: AUTHORNAME

AUTHORDESCRIPTION