English

Find the truth value of the following statement. It is not true that 3 − 7i is a real number.

Advertisements
Advertisements

Question

Find the truth value of the following statement.

It is not true that 3 − 7i is a real number.

Short/Brief Note
Advertisements

Solution

Let p : 3 – 7i is a real number.

The truth value of p is F.

The given statement in symbolic form is ~p.

∴ ~ p ≡ ~ F ≡ T

∴ Truth value of the given statement is T.

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Mathematical Logic - Exercise 1.4 [Page 11]

APPEARS IN

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

Write the following compound statement symbolically.

The angle is right angle if and only if it is of measure 90°.


Construct the truth table of the following statement pattern.

(p ∨ ∼ q) → (r ∧ p)


Construct the truth table of the following:

∼ (∼p ∧ ∼q) ∨ q


Express the following statement in symbolic form.

Mango is a fruit but potato is a vegetable.


Write the truth value of the following statement.

16 is an even number and 8 is a perfect square.


Write the truth value of the following statement.

The Himalayas are the highest mountains but they are part of India in the North East.


Write the negation of the following statement.

It is false that Nagpur is capital of Maharashtra


Write the following statement in symbolic form.

If triangle is equilateral then it is equiangular.


Find the truth value of the following statement.

Every accountant is free to apply his own accounting rules if and only if machinery is an asset.


Find the truth value of the following statement.

Neither 27 is a prime number nor divisible by 4.


Assuming that the following statement is true,

p : Sunday is holiday,

q : Ram does not study on holiday,

find the truth values of the following statements.

If Sunday is not holiday then Ram studies on holiday.


Fill in the blanks :

Conjunction of two statement p and q is symbolically written as ______.


Negation of “some men are animal” is ______.


State whether the following statement is True or False:

The negation of 10 + 20 = 30 is, it is false that 10 + 20 ≠ 30.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

To be brave is necessary and sufficient condition to climb the Mount Everest.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

If a real number is not rational, then it must be irrational.


Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)

If demand falls, then price does not increase.


Write the negation of the following.

Kanchanganga is in India and Everest is in Nepal.


Write the negation of the following.

If x ∈ A ∩ B, then x ∈ A and x ∈ B.


Rewrite the following statement without using the connective ‘If ... then’.

If it rains then the principal declares a holiday.


The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.


Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”


Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”


Let p : 7 is not greater than 4 and q : Paris is in France by two statements. Then ∼(p ∨ q) is the statement ______ 


The statement, 'If I go to school, then I will get knowledge' is equivalent to ______ 


Let S be a non-empty subset of R. Consider the following statement:

p: There is a rational number x ∈ S such that x > 0. Which of the following statements is the negation of the statement p? 


Express the following compound statement symbolically:

3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25


From the following set of statements, select two statements which have similar meaning.

  1. If a man is judge, then he is honest.
  2. If a man is not a judge, then he is not honest.
  3. If a man is honest, then he is a judge.
  4. If a man is not honest, then he is not a judge.

Let p: I am brave.
      q: I will climb the Mount Everest.

The symbolic form of a statement,

‘I am neither brave nor I will climb the mount Everest’ is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×