Advertisements
Advertisements
प्रश्न
Using truth tables, examine whether the statement pattern (p ∧ q) ∨ (p ∧ r) is a tautology, contradiction or contingency.
Advertisements
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
State which of the following is the statement. Justify. In case of a statement, state its truth value.
Zero is a complex number.
Write the truth values of the following.
64 is a perfect square and 46 is a prime number.
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
If the statement p, q are true statement and r, s are false statement then determine the truth value of the following:
(∼ r ↔ p) → ∼ q
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 such that x2 < 0
If A = {3, 5, 7, 9, 11, 12}, determine the truth value of the following.
∀ x ∈ A, 2x + 9 > 14
`sqrt5` is an irrational but `3sqrt5` is a complex number.
Write the truth value of the following statement:
∀ n ∈ N, n2 + n is even number while n2 – n is an odd number.
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.
`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.
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.
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.
Can you speak in English?
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 :
The statement (∼ p ∧ q) ∨∼ q 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
State whether the following statement is True or False :
Truth value of 2 + 3 < 6 is F.
State whether the following statement is True or False :
Dual of (p ∧ ∼ q) ∨ t is (p ∨ ∼ q) ∨ C.
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.
z is a positive number.
Solve the following :
State which of the following sentences are statements in logic.
(a + b)2 = a2 + 2ab + b2 for all a, b ∈ R.
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.
If stock prices are high then stocks are not rising.
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) → ∼ (q ∧ p)
If A = {2, 3, 4, 5, 6, 7, 8}, determine the truth value of the following statement.
∀ x ∈ A, x2 < 18.
If p is any statement then ( p ˅ ∼ p) is a
State the truth Value of x2 = 25
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 ______
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 q Λ ∼p is T, then which of the following is correct?
Using truth table prove that:
`p → (q ∨ r) ≡ (p → q) ∨ (p → r)`
