Implication

Q. Let p : Kiran passed the examination,
q : Kiran is sad
The symbolic form of a statement "It is not true that Kiran passed therefore he is sad' is

1. $\sim (p\leftrightarrow q)$
2. $(\sim p\to q)$
3. $(p\to q)$
4. $\sim (p\to \sim q)$

Q. The difference between the two roots of a quadratic equation is 2 and the difference between the cubes of the roots is 98, then find th quadratic equation?

Q.

Combine these two statements using, 'if and only if'

p:If a rectangle is a square, then all its four sides are equal.

q:If all the four sides of a rectangle are equal, then the rectangle is a square.

Q.

There are 25 days in a month. This is

1. a statement

2. a compound statement

3. a quantifier

4. an implication

Q. If $(p\wedge \sim r)\Rightarrow (q\wedge r)$ is false and q and r are both false, then p is ___.

1. False
2. May be true or false
3. Cannot conclude from given the information
4. True

Q.

The negation of the compound statement $p\vee (\sim p\vee q)$ is ___.

1. $(p\wedge \sim q)\vee \sim p$

2. $(p\wedge \sim q)\wedge \sim p$

3. $(\sim p\wedge \sim q)\wedge p$

4. $(p\vee \sim q)\wedge \sim p$

Q. Which of the following is logically equivalent to $\sim (\sim p\Rightarrow q)$

1. $p\wedge q$
2. $\sim p\wedge q$
3. $\sim p\wedge \sim q$
4. $p\wedge \sim q$

Q.

Which of the following are equivalent statements to the implication $p\to q$.

1. 

2. 

3. 

4. 

Q. Rewrite the following statement with “if-then” in five different ways conveying the same meaning. If a natural number is odd, then its square is also odd.

Q.

Which of the following is logically equivalent to $\sim (\sim p\Rightarrow q)?$

1. $p\wedge q$

2. $p\wedge \sim q$

3. $\sim p\wedge q$

4. $\sim p\wedge \sim q$

Q. Non zero complex number z is such that z +1/z is purely real

Q. The statement $p\to (q\to p)$ is equivalent to

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

Q.

Identify the false statement.

1. $\sim (p\vee \sim q)=\sim p\wedge q$

2. $\sim (p\vee q)=\sim p\vee \sim q$

3. $(p\wedge q)\wedge \sim p$ is a contradiction

4. $(p\vee q)\vee \sim p$ is a tautology

Q. Choose the best option to complete given sentence.
More people have ______ than we expected.

1. cast aside
2. turned up
3. carried out
4. came about

Q.

Write the contrapositive of the following statement.

'If you are born in India, then you are a citizen of India'.

Q.

Write contrapositive of the statement. "If you are born in India, then you are a citizen of India.

Q. Find out the error in the following sentence, if any. If there is no error, mark your answer as 'E.
I liked that opportune moment (A) when the workers proved their might (B) to take on the company (C) and came out victorious. No Error. (E)

1. A
2. B
3. C
4. D
5. E

Q. Can you cite any precedent in support of the case? No error.
(a) (b) (c) (d)

1. b
2. a
3. c
4. No error

Q. Find out the error in the following sentence, if any. If there is no error, mark your answer as 'E.
I know that eventually (A) he will succumb to me (B) and confess that he (C) has committed a crime. (D) No Error. (E)

1. A
2. B
3. C
4. D
5. E

Q. Find out the error in the following sentence, if any. If there is no error, mark your answer as 'E.
Under a tree (A) was sitting the saint (B) whom he had seen (C) somewhere else.(D) No Error. (E)

1. B
2. D
3. C
4. A
5. E

Q. Re write each of the following statements in the form “ p if and only if q ”. (i) p : If you watch television, then your mind is free and if your mind is free, then you watch television. (ii) q : For you to get an A grade, it is necessary and sufficient that you do all the homework regularly. (iii) r : If a quadrilateral is equiangular, then it is a rectangle and if a quadrilateral is a rectangle, then it is equiangular.

Q. Find out the error in the following sentence, if any. If there is no error, your answer is 'E'.
A new programme (A) is soon to be (B) telecast from the Delhi (C) Doordarshan. (D) No Error. (E)

1. C
2. E
3. D
4. A
5. B

Q.

Which of the following are equivalent statements to the implication $p\to q$.

1. $\sim q\to \sim p$

2. $p$ only if $q$

3. $p$ is a sufficient condition for $q$

4. $q$ is a necessary condition for $p$

Q. It is better to stay at home (A) than to walk in the street (B) when there is (C) a communal riot in the town. (D) No Error (E)

1. (A)
2. (B)
3. (C)
4. (D)
5. (E)

Q. Find out the error in the following sentence, if any. If there is no error, your answer is 'E'.
The conclusion will be arrived (A) but what we need (B) most is to have (C) patience and to wait. (D) No Error. (E)

1. A
2. B
3. E
4. D
5. C

Q. Write each of the statements in the form “if p , then q ”. (i) p : It is necessary to have a password to log on to the server. (ii) q : There is traffic jam whenever it rains. (iii) r : You can access the website only if you pay a subscription fee.

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

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

Q. Find out the error in the following sentence, if any. If there is no error, mark your answer as 'E.

1. B
2. D
3. C
4. A
5. E

Q.

What is the difference between mathematical deduction and induction?

Q. Find out the error in the following sentence, if any. If there is no error, mark your answer as 'E'.
All of them will execute (A) the plan so skilfully (B) that their officer (C) will feel surprised. (D) No Error. (E)

1. B
2. C
3. E
4. D
5. A