English

Write the Truth Value of the Negation of the Following Statement : - Mathematics and Statistics

Advertisements
Advertisements

Question

Write the truth value of the negation of the following statement : 

cos2 θ + sin2 θ = 1, for all θ ∈ R 

Sum

Solution

p : cos2 θ + sin2 θ = 1, for all θ ∈ R 

The truth value of p is T.

∴ The truth value of ~p is F

shaalaa.com
  Is there an error in this question or solution?
2015-2016 (July)

APPEARS IN

RELATED QUESTIONS

The negation of p ∧ (q → r) is ______________.


Without using the truth table show that P ↔ q ≡ (p ∧ q) ∨ (~ p ∧ ~ q)


Write the Truth Value of the Negation of the Following Statement :

The Sun sets in the East. 


Rewrite the following statement without using if ...... then.

If a man is a judge then he is honest.


Rewrite the following statement without using if ...... then.

It 2 is a rational number then `sqrt2` is irrational number.


Without using truth table prove that:

(p ∨ q) ∧ (p ∨ ∼ q) ≡ p


Without using truth table prove that:

∼ [(p ∨ ∼ q) → (p ∧ ∼ q)] ≡ (p ∨ ∼ q) ∧ (∼ p ∨ q)


Using rules in logic, prove the following:

p ↔ q ≡ ∼(p ∧ ∼q) ∧ ∼(q ∧ ∼p)


Using the rules in logic, write the negation of the following:

(p ∨ q) ∧ (q ∨ ∼r)


Using the rules in logic, write the negation of the following:

(p → q) ∧ r


Using the rules in logic, write the negation of the following:

(∼p ∧ q) ∨ (p ∧ ∼q)


Without using truth table, show that

p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)


Without using truth table, show that

p ∧ [(~ p ∨ q) ∨ ~ q] ≡ p


Without using truth table, show that

~ [(p ∧ q) → ~ q] ≡ p ∧ q


Without using truth table, show that

(p ∨ q) → r ≡ (p → r) ∧ (q → r)


Using the algebra of statement, prove that

(p ∧ q) ∨ (p ∧ ~ q) ∨ (~ p ∧ ~ q) ≡ (p ∨ ~ q)


Using the algebra of statement, prove that

(p ∨ q) ∧ (~ p ∨ ~ q) ≡ (p ∨ ~ q) ∧ (~ p ∨ q)


The statement pattern p ∧ ( q v ~ p) is equivalent to ______.


For any two statements p and q, the negation of the expression (p ∧ ∼q) ∧ ∼p is ______ 


(p → q) ∨ p is logically equivalent to ______ 


The logically equivalent statement of (p ∨ q) ∧ (p ∨ r) is ______ 


The statement pattern p ∧ (∼p ∧ q) is ______.


The statement pattern [∼r ∧ (p ∨ q) ∧ (p ∨ q) ∧ (∼p ∧ q)] is equivalent to ______ 


The negation of the Boolean expression (r ∧ ∼s) ∨ s is equivalent to: ______ 


The logical statement [∼(q ∨ ∼r) ∨ (p ∧ r)] ∧ (q ∨ p) is equivalent to: ______ 


Without using truth table prove that (p ∧ q) ∨ (∼ p ∧ q) v (p∧ ∼ q) ≡ p ∨ q


If p ∨ q is true, then the truth value of ∼ p ∧ ∼ q is ______.


Which of the following is not a statement?


∼ ((∼ p) ∧ q) is equal to ______.


Without using truth table, prove that:

[p ∧ (q ∨ r)] ∨ [∼r ∧ ∼q ∧ p] ≡ p


The statement p → (q → p) is equivalent to ______.


Show that the simplified form of (p ∧ q ∧ ∼ r) ∨ (r ∧ p ∧ q) ∨ (∼ p ∨ q) is q ∨ ∼ p.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×