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****MATHEMATICS REASONING QUIZ-8**

**MATHEMATICS REASONING QUIZ-8**

**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.**Which is not a statement?

**Q3.**Let p: is not greater than and q: Pairs is in France Be two statements. Then, ~(p∨q) is the statement

Solution

∼(p∨q)≡∼p∧∼q ∴ 7 is greater than 4 and Paris is not in France.

∼(p∨q)≡∼p∧∼q ∴ 7 is greater than 4 and Paris is not in France.

**Q5.**H:Set of holiday, S: Set of Sunday and U:Set of day's Then, the Venn diagram of statement, 'Every Sunday implies holiday' is

Solution

**Q7.**The negative of the proposition : “If a number is divisible by 15, then it is divisible by 5 or 3”

Solution

Consider the following statements: p= Number is divisible by 15 q= Number is divisible by 5 or 3 We have, p→q≅∼p∨q ∴∼(p→q)≅∼(∼p∨q)≅p∧∼q Clearly, p∧∼q is equivalent to: A number is divisible by 15 and it is not divisible by 5 and 3

Consider the following statements: p= Number is divisible by 15 q= Number is divisible by 5 or 3 We have, p→q≅∼p∨q ∴∼(p→q)≅∼(∼p∨q)≅p∧∼q Clearly, p∧∼q is equivalent to: A number is divisible by 15 and it is not divisible by 5 and 3

**Q8.**If p:A man is happy q:A man is rich Then, the statement, ""If a man is not happy, then he is not rich" is written as

Solution

∵p:A man is happy and q:A man is rich 'If a man is not happy, then he is not rich' is written as ∼p→∼q

∵p:A man is happy and q:A man is rich 'If a man is not happy, then he is not rich' is written as ∼p→∼q

**Q9.**Which of the following is a tautology?

**Q10.**~(p∨q)∨(~p∧q) is logically equivalent to

Solution

∼(p∨q)∨(∼p∧q)≡(∼p∧∼q)∨(∼p∧q) ≡∼p∧(∼q∨q)≡∼p∧t≡∼p

∼(p∨q)∨(∼p∧q)≡(∼p∧∼q)∨(∼p∧q) ≡∼p∧(∼q∨q)≡∼p∧t≡∼p