Advertisements
Advertisements
प्रश्न
Express the truth of the following statement by the Venn diagram.
Some members of the present Indian cricket are not committed.
Advertisements
उत्तर
U : The set of all human beings.
M : The set of all members of the present Indian cricket.
C : The set of all committed members of the present Indian cricket.
The above Venn diagram represents the truth of the given statement, i.e. C - M = Φ
APPEARS IN
संबंधित प्रश्न
Write the converse and contrapositive of the statement -
“If two triangles are congruent, then their areas are equal.”
Prove that the following statement pattern is a tautology : ( q → p ) v ( p → q )
Use the quantifiers to convert the following open sentence defined on N into true statement:
x2 ≥ 1
Examine whether the following statement (p ∧ q) ∨ (∼p ∨ ∼q) is a tautology or contradiction or neither of them.
Using the truth table prove the following logical equivalence.
(p ∨ q) → r ≡ (p → r) ∧ (q → r)
Examine whether the following statement pattern is a tautology or a contradiction or a contingency.
∼ (∼ q ∧ p) ∧ q
(p ∧ q) → r is logically equivalent to ________.
Inverse of statement pattern (p ∨ q) → (p ∧ q) is ________ .
Determine whether the following statement pattern is a tautology, contradiction or contingency:
[(p ∨ ∼q) ∨ (∼p ∧ q)] ∧ r
Prepare truth tables for the following statement pattern.
(~ p ∨ q) ∧ (~ p ∨ ~ q)
Prove that the following statement pattern is a tautology.
(p → q) ↔ (~ q → ~ p)
Show that the following statement pattern is contingency.
(p → q) ↔ (~ p ∨ q)
Using the truth table, verify
~(p ∨ q) ∨ (~ p ∧ q) ≡ ~ p
Prove that the following pair of statement pattern is equivalent.
~(p ∧ q) and ~p ∨ ~q
Write the dual statement of the following compound statement.
Karina is very good or everybody likes her.
Write the dual statement of the following compound statement.
Radha and Sushmita cannot read Urdu.
Write the converse, inverse, and contrapositive of the following statement.
"If it snows, then they do not drive the car"
Write the converse, inverse, and contrapositive of the following statement.
If he studies, then he will go to college.
What is tautology? What is contradiction?
Show that the negation of a tautology is a contradiction and the negation of a contradiction is a tautology.
Using the truth table, prove the following logical equivalence.
p ∧ (q ∨ r) ≡ (p ∧ q) ∨ (p ∧ r)
Using the truth table, prove the following logical equivalence.
[~(p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r
Using the truth table, prove the following logical equivalence.
~p ∧ q ≡ [(p ∨ q)] ∧ ~p
State the dual of the following statement by applying the principle of duality.
(p ∧ ~q) ∨ (~ p ∧ q) ≡ (p ∨ q) ∧ ~(p ∧ q)
Complete the truth table.
| p | q | r | q → r | r → p | (q → r) ˅ (r → p) |
| T | T | T | T | `square` | T |
| T | T | F | F | `square` | `square` |
| T | F | T | T | `square` | T |
| T | F | F | T | `square` | `square` |
| F | T | T | `square` | F | T |
| F | T | F | `square` | T | `square` |
| F | F | T | `square` | F | T |
| F | F | F | `square` | T | `square` |
The given statement pattern is a `square`
If p → (∼p v q) is false, then the truth values of p and q are respectively
The statement pattern (p ∧ q) ∧ [~ r v (p ∧ q)] v (~ p ∧ q) is equivalent to ______.
Which of the following is not equivalent to p → q.
Examine whether the following statement pattern is a tautology or a contradiction or a contingency:
(∼p ∧ ∼q) → (p → q)
If p, q are true statements and r, s are false statements, then find the truth value of ∼ [(p ∧ ∼ r) ∨ (∼ q ∨ s)].
