Advertisements
Advertisements
प्रश्न
Using truth tables, examine whether the statement pattern (p ∧ q) ∨ (p ∧ r) is a tautology, contradiction or contingency.
उत्तर
No of rows = 2n=23 =8
No. of columns = m+ n=3+3= 6
| p | q | r | p ∧ q | p ∧ r | (p ∧ q) ∨ (p ∧ r) |
| T | T | T | T | T | T |
| T | T | F | T | F | T |
| T | F | T | F | T | T |
| T | F | F | F | F | F |
| F | T | T | F | F | F |
| F | T | F | F | F | F |
| F | F | T | F | F | F |
| F | F | F | F | F | F |
In the last column, the truth values of the statement is neither all T nor all F. Hence, it is neither a tautology nor a contradiction i.e. it is a contingency.
APPEARS IN
संबंधित प्रश्न
Write truth values of the following statements :`sqrt5` is an irrational number but 3 +`sqrt 5` is a complex number.
Write truth values of the following statements: ∃ n ∈ N such that n + 5 > 10.
State which of the following is the statement. Justify. In case of a statement, state its truth value.
Zero is a complex number.
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.
A quadratic equation cannot have more than two roots.
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.
Can you speak in Marathi?
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.
4 is odd or 1 is prime.
Write the truth values of the following.
5 is a prime number and 7 divides 94.
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 → p) → (∼ s ∨ r)]
If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:
∼ [(∼ p ∧ r) ∨ (s → ∼ q)] ↔ (p ∧ r)
If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.
∀ x ∈ A, x2 + x is an even number
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
If p ∧ q is F, p → q is F then the truth values of p and q are ________.
Which of the following sentence is the statement in logic? Justify. Write down the truth value of the statement:
4! = 24.
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.
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.
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.
Please grant me a loan.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
x2 − 6x + 8 = 0 implies x = −4 or x = −2.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Did you eat lunch yet?
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.
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.
3 + 5 > 11
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.
State which of the following sentence is a statement. Justify your answer if it is a statement. Write down its truth value.
Can you speak in English?
Which of the following statements is false?
Choose the correct alternative :
For the following three statements
p : 2 is an even number.
q : 2 is a prime number.
r : Sum of two prime numbers is always even.
Then, the symbolic statement (p ∧ q) → ∼ r means.
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
Choose the correct alternative :
If p is the sentence ‘This statement is false’ then
Choose the correct alternative :
Conditional p → q is equivalent to
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 –––––––––.
Fill in the blanks :
Truth value of 2 + 3 = 5 if and only if − 3 > − 9 is –––––––––.
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 “John and Ayub went to the forest” is “John and Ayub went to the forest”.
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.
Read a lot to improve your writing skill.
Solve the following :
State which of the following sentences are statements in logic.
z is a positive number.
Solve the following :
State which of the following sentences are statements in logic.
(2 + 1)2 = 9.
Solve the following :
State which of the following sentences are statements in logic.
Why are you sad?
Solve the following :
State which of the following sentences are statements in logic.
Do not come inside the room.
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.
Please carry out my instruction.
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.
(x − 2) (x − 3) = x2 − 5x + 6 for all x∈R.
Determine the truth value of the following statement.
If 9 > 1 then x2 − 2x + 1 = 0 for x = 1
Determine the truth value of the following statement.
x + y = 0 is the equation of a straight line if and only if y2 = 4x is the equation of the parabola.
Assuming the following statement.
p : Stock prices are high.
q : Stocks are rising.
to be true, find the truth value of the following.
Stock prices are not high or stocks are rising.
Assuming the following statement.
p : Stock prices are high.
q : Stocks are rising.
to be true, find the truth value of the following.
If stock prices are high then stocks are not rising.
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.
If p, q, r are statements with truth values T, T, F respectively determine the truth values of the following.
p ↔ (q → ∼ p)
If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.
∃ x ∈ A, such that 3x + 2 > 9
If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.
∀ x ∈ A, x2 < 18.
Which of the following statement is true
State the truth value of `sqrt(3)` is not an irrational number
State the truth value of (p ˄ ∼p)
State whether the following statement is True or False:
(p ˅ q) ˄ ~ p is a contradiction
State whether the following statement is True or False:
The dual of (p ˄ q) ˅ ~ q is (p ˅ q) ˄ ~ q
State whether the following statement is True or False:
p ˅ ~ p ≡ ~ c
The truth value of the statement “Neither 27 is a prime number nor divisible by 4” is ______
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r).
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` |
If p ↔ (~ p → q) is false, then the truth values of p and q are respectively ______.
