Advertisements
Advertisements
Question
If p, q, r are the statements with truth values T, F, T, respectively then find the truth value of (r ∧ q) ↔ ∼ p
Advertisements
Solution
(r ∧ q) ↔ ∼ p
≡ (T ∧ F) ↔ ∼T
≡(T ∧ F) ↔ F [1]
≡ F ↔ F
≡ T
Hence, the truth value is ‘T’
APPEARS IN
RELATED QUESTIONS
Write truth values of the following statements :`sqrt5` is an irrational number but 3 +`sqrt 5` is a complex number.
State which of the following is the statement. Justify. In case of a statement, state its truth value.
Do you like Mathematics?
State which of the following is the statement. Justify. In case of a statement, state its truth value.
It rains heavily.
Write the truth values of the following.
5 is a prime number and 7 divides 94.
Write the truth values of the following.
It is not true that 5−3i is a real number.
If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:
(p → q) ∨ (r → s)
If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:
(p → q) ∧ ∼ r
If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:
[∼ p ∧ (∼ q ∧ r)] ∨ [(q ∧ r) ∨ (p ∧ r)]
If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.
∃ x ∈ A such that x – 8 = 1
If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.
∀ x ∈ A, x2 + x is an even number
Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:
4! = 24.
`sqrt5` is an irrational but `3sqrt5` is a complex number.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
A triangle has ‘n’ sides.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
The sum of interior angles of a triangle is 180°
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
`sqrt(-4)` is an irrational number.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
The number 2 is the only even prime number.
The negation of the proposition “If 2 is prime, then 3 is odd”, is ______.
Fill in the blanks :
The statement q → p is called as the ––––––––– of the statement p → q.
State whether the following statement is True or False :
There are 24 months in year is a statement.
State whether the following statement is True or False :
Dual of (p ∧ ∼ q) ∨ t is (p ∨ ∼ q) ∨ C.
State whether the following statement is True or False :
“His birthday is on 29th February” is not a statement.
Solve the following :
State which of the following sentences are statements in logic.
If x is real number then x2 ≥ 0.
Which of the following sentence is a statement? In case of a statement, write down the truth value.
What are the causes of rural unemployment?
Assuming the following statement.
p : Stock prices are high.
q : Stocks are rising.
to be true, find the truth value of the following.
It is false that stocks are rising and stock prices are high.
If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.
∀ x ∈ A, x2 + 2 ≥ 5.
State the truth value of `sqrt(3)` is not an irrational number
Choose the correct alternative :
Which of the following statement is true?
Choose the correct alternative :
Which of the following is not a statement?
State whether the following statement is True or False:
Mathematical identities are true statements
The truth value of negation of “London is in England” is ______
The truth value of the statement “Neither 27 is a prime number nor divisible by 4” is ______
Using truth table prove that ~ p ˄ q ≡ ( p ˅ q) ˄ ~ p
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r).
Without using truth table show that
(p ∨ q) ∧ (~ p ∨ ~ q) ≡ (p ∧ ~ q) ∨ ( ~ p ∧ q)
If p ↔ q and p → q both are true, then find truth values of the following with the help of activity
p ˅ q
|
p ↔ q and p → q both are true if p and q has truth value `square`, `square` or `square`, `square`. p ˅ q i. If both p and q are true, then p ˅ q = `square` ˅ `square` = `square` ii. If both p and q are false, then p ˅ q = `square` ˅ `square` = `square` |
If p : Every square is a rectangle. q : Every rhombus is a kite, then truth values of p `rightarrow` q and p `leftrightarrow` q are ______ and ______ respectively.
