Advertisements
Advertisements
Question
Write the truth value of the following.
Milk is white if and only if sky is blue.
Solution
Let p: Milk is white.
q: Sky is blue
Then the symbolic form of the given statement is p↔q.
The truth values of both p and q are T.
∴ The truth value of p↔q is T .......[T↔T ≡ T]
APPEARS IN
RELATED QUESTIONS
State which of the following is the statement. Justify. In case of a statement, state its truth value.
5 + 4 = 13
State which of the following is the statement. Justify. In case of a statement, state its truth value.
x – 3 = 14
State which of the following is the statement. Justify. In case of a statement, state its truth value.
Close the door.
State which of the following is the statement. Justify. In case of a statement, state its truth value.
Please get me breakfast.
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.
All real numbers are whole numbers.
State which of the following is the statement. Justify. In case of a statement, state its truth value.
Can you speak in Marathi?
State which of the following is the statement. Justify. In case of a statement, state its truth value.
The sum of cube roots of unity is zero.
Write the truth values of the following.
24 is a composite number or 17 is a prime number.
If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:
(q ∧ r) ∨ (∼ p ∧ 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] ∨ [(q → p) → (∼ s ∨ 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 such that x2 < 0
If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.
∀ x ∈ A, x is an even number.
If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.
∀ x ∈ A, 2x + 9 > 14
Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:
4! = 24.
Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:
India is a country and Himalayas is a river.
Write the truth value of the following statement:
The square of any even number is odd or the cube of any odd number is odd.
Write the truth value of the following statement:
∀ n ∈ N, n + 6 > 8.
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.
You are amazing!
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.
Have a cup of cappuccino.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Every real number 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.
1 is a prime number.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
With the sunset the day ends.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
The number π 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.
Bring the motor car here.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
It may rain today.
Which of the following is not a statement?
Which of the following statements is false?
Choose the correct alternative :
If p : He is intelligent.
q : He is strong
Then, symbolic form of statement “It is wrong that, he is intelligent or strong” is
If p and q are two statements then (p → q) ↔ (∼ q → ∼ p) is ______.
Choose the correct alternative :
Conditional p → q is equivalent to
Choose the correct alternative :
Negation of the statement “This is false or That is true” is
Fill in the blanks :
The statement q → p is called as the ––––––––– of the statement p → q.
If p ∨ q is true then truth value of ∼ p ∨ ∼ q is ______.
Fill in the blanks :
p ↔ q is false when p and q have ––––––––– truth values.
Fill in the blanks :
Let p : the problem is easy. r : It is not challenging then verbal form of ∼ p → r is –––––––––.
State whether the following statement is True or False :
p ∨ q has truth value F is both p and q has truth value F.
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 :
p ∧ t = p.
Solve the following :
State which of the following sentences are statements in logic.
Ice cream Sundaes are my favourite.
Solve the following :
State which of the following sentences are statements in logic.
x + 3 = 8 ; x is variable.
Solve the following :
State which of the following sentences are statements in logic.
Read a lot to improve your writing skill.
Solve the following :
State which of the following sentences are statements in logic.
The square of any odd number is even.
Solve the following :
State which of the following sentences are statements in logic.
If x is real number then x2 ≥ 0.
Solve the following :
State which of the following sentences are statements in logic.
What a horrible sight it was!
Which of the following sentence is a statement? In case of a statement, write down the truth value.
The Himalayas is the highest mountain range.
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?
Determine the truth value of the following statement.
If 9 > 1 then x2 − 2x + 1 = 0 for x = 1
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 p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.
(p ∧ q) → ∼ p.
State the truth value of (p ˅ ∼p)
If statements p, q are true and r, s are false, determine the truth values of the following.
~ p ∧ (q ∨ ~ r)
The dual of the statement (p ˅ q) ˄ (r ˅ s) is ______.
State whether the following statement is True or False:
p → q is equivalent to p → ~ q
State whether the following statement is True or False:
(p ˅ q) ˄ ~ p is a contradiction
State whether the following statement is True or False:
Mathematical identities are true statements
State whether the following statement is True or False:
p ˅ ~ p ≡ ~ c
Using truth table prove that ~ p ˄ q ≡ ( p ˅ q) ˄ ~ p
Given following statements
p: 9 × 5 = 45
q: Pune is in Maharashtra
r: 3 is the smallest prime number
Write truth values by activity
|
i) (p ˄ q) ˄ r = `(square` ˄ `square)` ˄ `square` = `square` ˄ `square` = `square` ii) ~ ( p ˄ r ) = `~(square` ˄ `square)` = `~ square` = `square` iii) p → q = `square → square` = `square` |
Which of the following quantified statement is true?
Let a: ~ (p ∧ ~ r) v (~ q v s) and
b: (p v s) ↔ (q ∧ r).
If the truth values of p and q are true and that of rands are false, then the truth values of a and bare respectively.
The negation of 'For every real number x, `x^2 ≥ 0`' is ______
If (p ∧ ~ q) → ~ p is false, the truth values of p and q are respectively.
Using truth table prove that:
`p → (q ∨ r) ≡ (p → q) ∨ (p → r)`
Find the truth value of the following compound statement:
5 + 4 = 9 and 6 × 3 = 12
