हिंदी

Discuss the statement pattern, using truth table : ~(~p ∧ ~q) v q

Advertisements
Advertisements

प्रश्न

Examine whether each of the following statement patterns is a tautology or a contradiction or a contingency.

[~(~p ∧ ~q)] v q

योग
Advertisements

उत्तर

Consider the statement pattern: ∼ (∼ p ∧ ∼ q) ∨ q
Thus the truth table of the given logical statement: ~(~p ∧ ~q) ∨ q

p q ~p ~q ~p∧~q ~(~p ∧ ~q) ~(~p ∧ ~q) ∨ q
T T F F F T T
T F F T F T T
F T T F F T T
F F T T T F F

The above statement is contingency.

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 3.03 | पृष्ठ १३

वीडियो ट्यूटोरियलVIEW ALL [3]

संबंधित प्रश्न

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.

Nagpur is in Maharashtra and Chennai is in Tamil Nadu. 


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.

x is not irrational number but is a square of an integer.


Construct the truth table of the following statement pattern.

(p ∧ q) ↔ (q ∨ r)


If p ∧ q is false and p ∨ q is true, then ______ is not true.


Construct the truth table of the following:

p → (q → p)


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.


Express the following statement in symbolic form.

I like playing but not singing.


Write the truth value of the following statement.

16 is an even number and 8 is a perfect square.


Write the negation of the following statement.

All men are animals.


Write the following statement in symbolic form.

Milk is white if and only if the sky is not blue.


Find the truth value of the following statement.

It is not true that 3 − 7i 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) ↔ ~(p ∨ q)


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

~ [p ∨ (r ∧ s)] ∧ ~ [(r ∧ ~ s) ∧ 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.

Sunday is a holiday and 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.

The Sun has set and Moon has risen.


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 ∨ r)


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) ∧ ∼ r


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) ∧ r


Write the negation of the following.

An angle is a right angle if and only if it is of measure 90°.


Write the negation of the following statement.

∀ n ∈ N, n + 3 > 9.


A biconditional statement is the conjunction of two ______ statements.


Write the following compound statements symbolically.

Triangle is equilateral or isosceles


Without using truth table show that -

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


If p : Every natural number is a real number.
q : Every integer is a complex number. Then truth values of p → q and p ↔ q are ______ and ______ respectively.


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


Which of the following is false?


The negation of (p ∨ ∼q) ∧ q is ______


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? 


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:

Delhi is in India but Dhaka is not in Sri Lanka


Write the contrapositive of the inverse of the statement:

‘If two numbers are not equal, then their squares are not equal’.


Write the negation of p ↔ q.


Using truth table prove that:

~ (p `leftrightarrow` q) ≡ (p ∧ ~ q) ∨ (q ∧ ~ p)


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×