# Implication

## Trending Questions

**Q.**Negation of the statement p→(q ∨ r) is

- ∼p→∼(q ∨ r)
- ∼p→∼(q ∧ r)
- (q ∨ r)→ p
- p ∧ (∼q ∧∼r)

**Q.**Three schools A, B and C organized a mela for collecting funds for helping the rehabilitation of flood victims. They sold hand made fans, mats and plates from recycled material at a cost of Rs. 25, Rs.100, and Rs. 50 each. The number of articles sold are given below:

Find the funds collected by each school separetly by selling the above articles. Also find the total funds collected for the purpose.

Write one value generated by the above situation.

**Q.**Divide sum of 6512 and 83 by their differences.

**Q.**Negation of the compound proposition : If I study hard, then I will pass.

- I will study hard or I shall pass.
- I will study hard or I shall not pass.
- I will study hard and I will not pass.
- I will study hard and I will pass.

**Q.**If truth value for p→(q∨r) is false, then the truth values of p, q, r are respectively :

- F, F, F
- T, F, F
- F, F, T
- T, T, F

**Q.**

Which of the following is the inverse of the proposition: “If a number is a prime then it is odd”?

If a number is not a prime then it is odd

If a number is not a prime then it is not odd

If a number is not odd then it is not a prime

If a number is not odd then it is a prime

**Q.**The negation of the statement "if 5>7 then, 6<4"

- (5>7) ∧ (6≥4)
- (5>7) ∨ (6≤4)
- (5≤7) ∨ (6≤4)
- (5≤7) ∧ (6≤4)

**Q.**The irrational number among the following is

- 3.5
- √3
- 59
- 0.007

**Q.**

Which of the following is a contradiction?

$\left(p\wedge q\right)\wedge ~\left(p\vee q\right)$

$p\vee \left(~p\wedge q\right)$

$\left(p\Rightarrow q\right)\Rightarrow p$

None of these

**Q.**

Negation of the compound proposition: If the examination is difficult, then I shall pass if I study hard

The examination is difficult and I study hard and I shall pass

The examination is difficult and I study hard but I shall not pass

The examination is not difficult and I study hard and I shall pass

None of these

**Q.**

The proposition $\left(p\Rightarrow ~p\right)\wedge \left(~p\Rightarrow p\right)$ is a

Tautology and contradiction

Neither tautology nor contradiction

Contradiction

Tautology

**Q.**f(x)=1q if x=pq where p and q are integer and q≠0, G.C.D of (p, q) = 1 and f(x) = 0 if x is irrational then set of continuous points of f(x) is

- All integers
- All real numbers
- All rational numbers
- All irrational number

**Q.**Let p and q be any two logical statements and r be the statement p→(∼p∨q). If r has the truth value F, then the truth values of p and q are, respectively

- F, F
- T, T
- F, T
- T, F

**Q.**If the equation ax+2x-2=0 has real and distinct roots then value of a is?

**Q.**If p, q, r have truth values T, F, T respectively, then which among the following will have truth value as TRUE.

- (p→q)∧r
- (p→q)∨q
- (p∧q)∧(p∨r)
- q→(p∧r)

**Q.**The negation of the proposition: "If a number is divisible by 15, then it is divisible by 5 or 3" is

- If a number is divisible by 15 then it is not divisible by 5 and 3
- A number is divisible by 15 and it is not divisible by 5 and 3.
- A number is not divisible by 15 or it is divisible by 5 or 3.
- A number is not divisible by 15 or it is not divisible by 5 and 3

**Q.**Let A be the set of two positive integers. Let f : A --> set of positive integers be defined by

f(n) = p, where p is the highest prime factor of n

If range of f = {3}. Find set A. Is A uniquely determined?

**Q.**If truth value for p→(q∨r) is false, then the truth values of p, q, r are respectively :

- T, F, F
- F, F, F
- F, F, T
- T, T, F

**Q.**

Which of the following is not true for any two statements $p$ and $q$?

$~\left[p\vee \left(~q\right)\right]\equiv \left(~p\right)\wedge q$

$~(p\vee q)=(~p)\vee (~q)$

$q\wedge ~q$

$~[p\wedge (~p\left)\right]$

**Q.**Negation of the statement "If △ABC is isosceles then the base angle's A and B are equal" , is

- △ABC is isosceles and the base angles A and B are not equal.
- △ABC is not isosceles and the base angles A and B are not equal.
- △ABC is not isosceles and the base angles A and B are equal.
- △ABC is not isosceles or the base angles A and B are not equal.

**Q.**The logical statement (p⇒q)∧(q⇒∼p) is equivalent to

- ∼p
- p
- q
- ∼q

**Q.**The statement (p ∨∼q)∧(∼p∨q) is

- a fallacy
- a tautology
- logically equivalent to p∧q
- neither a fallacy nor a tautology

**Q.**If p and q are substatements "A natural number is odd " and "A natural number is not divisible by 2"respectively, then the biconditional statement p⇔q is

- A natural number is odd, if and only if it is divisible by 2.
- A natural number is odd, if and only if it is not divisible by 2.
- If a natural number is odd, then it is not divisible by 2.
- If a natural number is odd, then it is divisible by 2.

**Q.**

What is the abstract noun of the word Need?

**Q.**Which of the following is not equivalent form of compound statement formed by the logical connective "if and only if" using the sub statements p and q

- if p, then q
- q if and only if p
- p if and only if q
- p is necessary and sufficient condition for q and vice - versa

**Q.**Considering truth table for p→∼(p∧∼q) as follows,

pqp→∼(p∧∼q)TTATFBFTCFFD

The truth value will be false for which among the following

- A
- B
- C
- D

**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

- (∼p→q)
- (p→q)
- ∼(p→∼q)
- ∼(p↔q)

**Q.**

Show that area of the prallelogram whose diagonals are given by →a and →b is →a×→b2. Also, find the area of the parallelogram, whose diagonals are 2^i−^j+k and ^i+3^j−^k.

**Q.**

Can l' hospital rule be applied to function giving (infinity/infinity) form?

**Q.**ntFind the Bi-quadratic equation with rational coefficients whose one of the root is 2+-3n