Test: Implications And Validating Of Statements

# Test: Implications And Validating Of Statements - Commerce

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## 10 Questions MCQ Test Mathematics (Maths) Class 11 - Test: Implications And Validating Of Statements

Test: Implications And Validating Of Statements for Commerce 2023 is part of Mathematics (Maths) Class 11 preparation. The Test: Implications And Validating Of Statements questions and answers have been prepared according to the Commerce exam syllabus.The Test: Implications And Validating Of Statements MCQs are made for Commerce 2023 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Implications And Validating Of Statements below.
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Test: Implications And Validating Of Statements - Question 1

### Two pairs of statement are: p: If a quadrilateral is a rectangle, then its opposite sides are equal. q: If opposite sides of a quadrilateral are equal, then the quadrilateral is a rectangle. The combined statement of these pairs using “If and only if” is:

Detailed Solution for Test: Implications And Validating Of Statements - Question 1

‘A quadrilateral is a rectangle if and only if its opposite sides are equal’ because statements p & q are satisfied in this combined statement.

Test: Implications And Validating Of Statements - Question 2

### Write the contra positive of the given statement If -7 < 0 then 7 > 0

Detailed Solution for Test: Implications And Validating Of Statements - Question 2

Test: Implications And Validating Of Statements - Question 3

### The contra positive of a statement p ⇒ q, is the statement

Detailed Solution for Test: Implications And Validating Of Statements - Question 3

Contraceptive of a→b is ∼b→∼a
Then,Contraceptive of p→(∼q→∼r)
≡∼(∼q→∼r)→∼p
≡∼(q∧∼r)→∼p[a→b≡∼a∧b]
≡(∼q∨r)→∼p  [Demorgas law]

Test: Implications And Validating Of Statements - Question 4

Name the technique used in the first step of the soluntion of the problem below :
Verify that √5 is irrational
Solution ; Let us assume that √5 is rational

Test: Implications And Validating Of Statements - Question 5

If p and q are mathematical statements, then in order to show that the statement “p and q” is true, we need to show that:

*Multiple options can be correct
Test: Implications And Validating Of Statements - Question 6

In order to prove the statement “If p then q” we need to show that:

Detailed Solution for Test: Implications And Validating Of Statements - Question 6

Case 1: By assuming that p is true, prove that q must be true.(Direct method)
Case 2 :  By assuming that q is false, prove that p must be false.(Contrapositive Method)

Test: Implications And Validating Of Statements - Question 7

In order to prove the statement “p if and only if q” we need to show:

Detailed Solution for Test: Implications And Validating Of Statements - Question 7

In order to prove the statement “p if and only if q”, we need to show.

• If p is true, then q is true and
• If q is true, then p is true.
Test: Implications And Validating Of Statements - Question 8

The component statements are:
p: You are wet when it rains.
q: You are wet when you are in river.
The compound statement of these component statements using appropriate connective is:

Test: Implications And Validating Of Statements - Question 9

Which option is not same as “if p then q”?

Test: Implications And Validating Of Statements - Question 10

Name the technique used in the solution of the problems below :
Question: Show that the following statement is false: If n is an odd integer, then n is prime.
Solution: The given statement is in the form “if p then q” we have to show that this is false, If p then ~q.
n = 99 is odd integer which is not a prime number. Thus, we conclude that the given statement is false.

Detailed Solution for Test: Implications And Validating Of Statements - Question 10

Here n = 99 is a counter example of the given statement.
Therefore,
Option A

## Mathematics (Maths) Class 11

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## Mathematics (Maths) Class 11

157 videos|210 docs|132 tests