हिंदी

Construct the truth table of the following statement pattern. (p ∧ ∼q) ↔ (p → q)

Advertisements
Advertisements

प्रश्न

Construct the truth table of the following statement pattern.

(p ∧ ∼q) ↔ (p → q)

सारिणी
Advertisements

उत्तर

p q ∼q p ∧ ∼ q p → q (p ∧ ∼q) ↔ (p → q)
T T F F T F
T F T T F F
F T F F T F
F F T F T F
shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Mathematical Logic - Exercise 1.2 [पृष्ठ १३]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Arts and Science) [English] Standard 12 Maharashtra State Board
अध्याय 1 Mathematical Logic
Exercise 1.2 | Q 1.02 | पृष्ठ १३

वीडियो ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्न

Using truth table prove that p ↔ q = (p ∧ q) ∨ (~p ∧ ~q).


Using truth table, prove the following logical equivalence:

(p ∧ q) → r ≡ p → (q → r)


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.

If ΔABC is right-angled at B, then m∠A + m∠C = 90°.


Construct the truth table of the following statement pattern.

p → [∼ (q ∧ r)]


Construct the truth table of the following statement pattern.

(∼ p → ∼ q) ∧ (∼ q → ∼ p)


Construct the truth table of the following statement pattern.

[p → (q → r)] ↔ [(p ∧ q) → r]


Determine the truth values of p and q in the following case:

(p ∨ q) is T and (p ∨ q) → q is F


Write the negation of the following statement.

2 + 3 ≠ 5


Write the truth value of the negation of the following statement.

London is in England.


Write the following statement in symbolic form.

It is not true that “i” is a real number.


Find the truth value of the following statement.

If a joint venture is a temporary partnership, then discount on purchase is credited to the supplier.


Find the truth value of the following statement.

3 is a prime number and an odd number.


If p and q are true and r and s are false, find the truth value of the following compound statement.

(p → q) ∨ (r ∧ s) 


If p and q are true and r and s are false, find the truth value of the following compound statement.

~ [(~ p ∨ s) ∧ (~ q ∧ r)]


If p and q are true and r and s are false, find the truth value of the following compound statement.

(p → q) ↔ ~(p ∨ q)


Assuming that the following statement is true,

p : Sunday is holiday,

q : Ram does not study on holiday,

find the truth values of the following statements.

If Sunday is not holiday then Ram studies on holiday.


Negation of “some men are animal” is ______.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

3 is prime number if 3 is perfect square number.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

To be brave is necessary and sufficient condition to climb the Mount Everest.


Assuming the first statement p and second as q. Write the following statement in symbolic form.

The drug is effective though it has side effects.


If p : Proof is lengthy.
q : It is interesting.
Express the following statement in symbolic form.

Proof is lengthy and it is not interesting.


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


Write the negation of the following.

Kanchanganga is in India and Everest is in Nepal.


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 high or stocks are not rising iff stocks are rising.


Write the negation of the following statement.

7 is prime number and Tajmahal is in Agra.


Write the negation of the following statement.

I will have tea or coffee.


The negation of the statement (p ˄ q) `→` (r ˅ ∼ p) is ______.


Write the following compound statements symbolically.

Triangle is equilateral or isosceles


Without using truth table prove that:

~ (p ∨ q) ∨ (~ p ∧ q) ≡ ~ p


Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”


Write the following statements in symbolic form

If Kutab – Minar is in Delhi then Taj - Mahal is in Agra


Without using truth table show that -

(p ˅ q) ˄ (∼p v ∼q) ≡ (p ∧ ∼q) ˄ (∼p ∧ q)


Write the negation of p → q


Write the following statements in symbolic form.

If Qutub – Minar is in Delhi then Taj-Mahal is in Agra


If (p ∧ ~ r) → (~ p ∨ q) is a false statement, then respective truth values of p, q and r are ______.


If p and q are true and rands are false statements, then which of the following is true?


The negation of the statement: "Getting above 95% marks is a necessary condition for Hema to get admission in good college'' is ______


The logical statement (∼p → q) ∧ (q → p) is equivalent to: ______ 


Conditional of p → q is equivalent to p → ∼ q.


Converse of the statement q `rightarrow` p is ______.


Write the following statement in symbolic form.

It is not true that `sqrt(2)` is a rational number.


Write the following statement in symbolic form.

4 is an odd number if 3 is not a prime factor of 6.


The statement ∼(p ↔ ∼q) is ______.


Express the following compound statement symbolically:

3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25


Construct the truth table for the statement pattern:

[(p → q) ∧ q] → p


Let p: I am brave.
      q: I will climb the Mount Everest.

The symbolic form of a statement,

‘I am neither brave nor I will climb the mount Everest’ is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×