Validation of Statement

Q.

By using the method of contradiction verify that $\sqrt{5}$ is irrational.

Q.

If $p\Rightarrow (q\vee r)$ is false, then the truth values of p, q, r are respectively

1. T, F, F

2. F, T, T

3. F, F, F

4. T, T, T

Q.

If p and q are simple statements, $p\iff \sim q$ is true when

1. p is true and q is true

2. Both p and q are false

3. p is false and q is true

4. p is true and q is false

Q.

Write whether the following statements are True or False? Justify your answer:

The things which are double of the same thing are equal to one another.

1. True
2. False

Q. If $p\Rightarrow (q\vee r)$ is false, then the truth values of p, q, r are respectively

1. T, F, F
2. F, F, F
3. F, T, T
4. T, T, T

Q. Which of the following statements are true and which are false? In each case give a valid reason for saying so. (i) p : Each radius of a circle is a chord of the circle. (ii) q : The centre of a circle bisects each chord of the circle. (iii) r : Circle is a particular case of an ellipse. (iv) s : If x and y are integers such that x > y , then – x < – y . (v) t : is a rational number.

Q.

If p and q are simple statements, $p\iff \sim q$ is true when

1. p is true and q is true

2. Both p and q are false

3. p is false and q is true

4. none of these

Q.

If $p\Rightarrow (q\vee r)$ is false, then the truth values of p, q, r are respectively

1. T, F, F

2. F, F, F

3. F, T, T

4. T, T, T

Q. The logically equivalent proposition of $p\leftrightarrow q$ is

1. $(p\to q)\wedge (q\to p)$
2. $(p\to q)\vee (q\to p)$
3. $(p\wedge q)\to (p\vee q)$
4. $(p\wedge q)\vee (p\vee q)$

Q.

If A = {0, 1}, B = {x: x is a binary number} then

1. 

2. 

3. 

4. 

Q.

Sivaang made the statement "a prime number is always odd”. Dylan replied "2 is a prime number and its an even number”. By which method did Dylan validate/disprove Sivaang's statement?

1. Contradiction

2. None of these

3. Direct

4. Contrapositive

Q. $\mathrm{The}\mathrm{contrapositive}\mathrm{of\; p\; \to \; \neg q}\mathrm{is}$.

1. $q\to \neg p$
2. $\neg q\to \neg p$
3. $q\to p$
4. $p\to q$

Q. If $p\equiv$ "It rains today", $q\equiv$ "I go to school", $r\equiv$ "I shall meet my friends"
What can be concluded from "If it rains I won't go to school, instead I will meet my friends." ?

1. $r\wedge \sim q\Rightarrow \sim p$
   
2. $q\vee \sim r\Rightarrow \sim p$
   
3. $p\Rightarrow q\wedge r$
   
4. $p\Rightarrow q\vee r$

Q. p $\vee$ q is true $⟺$ Exactly one of p or q is true.

1. False
2. True