Advertisements
Advertisements
Question
Consider the following statements.
- If D is dog, then D is very good.
- If D is very good, then D is dog.
- If D is not very good, then D is not a dog.
- If D is not a dog, then D is not very good.
Identify the pairs of statements having the same meaning. Justify.
Advertisements
Solution
Let p : D is dog.
q : D is very good.
Then the given statement in the symbolic form is
- p → q
- q → p
- ~q → ~p
- ~p → ~q
| p | q | ~p | ~q | p → q | q → p | ~q → ~p | ~p → ~q |
| T | T | F | F | T | T | T | T |
| T | F | F | T | F | T | F | T |
| F | T | T | F | T | F | T | F |
| F | F | T | T | T | T | T | T |
Since the entries in (i) and (iii) columns are the same, they have the same meaning.
Also, the entries in (ii) and (iv) columns are the same. they have the same meaning.
RELATED QUESTIONS
Write down the following statements in symbolic form :
(A) A triangle is equilateral if and only if it is equiangular.
(B) Price increases and demand falls
Write the following compound statement symbolically.
The angle is right angle if and only if it is of measure 90°.
Write the following compound statement symbolically.
Hima Das wins gold medal if and only if she runs fast.
Write the following compound statement symbolically.
x is not irrational number but is a square of an integer.
If p ∧ q is false and p ∨ q is true, then ______ is not true.
Determine the truth values of p and q in the following case:
(p ∨ q) is T and (p ∧ q) is T
Determine the truth values of p and q in the following case:
(p ∧ q) is F and (p ∧ q) → q is T
Express the following statement in symbolic form.
Milk is white or grass is green.
Write the negation of the following statement.
It is false that Nagpur is capital of Maharashtra
Write the truth value of the negation of the following statement.
London is in England.
Write the following statement in symbolic form.
Even though it is not cloudy, it is still raining.
Write the following statement in symbolic form.
Stock prices are high if and only if stocks are rising.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
The Sun has set and Moon has risen.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
If Kiran drives the car, then Sameer will walk.
Assuming the first statement p and second as q. Write the following statement in symbolic form.
x3 + y3 = (x + y)3 if xy = 0.
If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.
It is not true that the proof is lengthy but it is interesting.
Let p : Sachin wins the match.
q : Sachin is a member of Rajya Sabha.
r : Sachin is happy.
Write the verbal statement of the following.
p → q
Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)
If demand falls, then price does not increase.
Write the negation of the following.
If ∆ABC is not equilateral, then it is not equiangular.
Without using truth table show that -
(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)
Write the following statements in symbolic form.
If Qutub – Minar is in Delhi then Taj-Mahal is in Agra
The symbolic form of the following circuit is (where p, q represents switches S1 and S2 closed respectively)
Which of the following is NOT true for p → q.
The Boolean expression ∼(q ⇒ ∼p) is equivalent to: ______
Let S be a non-empty subset of R. Consider the following statement:
p: There is a rational number x ∈ S such that x > 0. Which of the following statements is the negation of the statement p?
The negation of the statement: "Getting above 95% marks is a necessary condition for Hema to get admission in good college'' is ______
If a statement b has truth value False and \[(p\wedge q)\leftrightarrow r\] has truth value True, then which of the following has truth value True?
