हिंदी

Construct the truth table of the following statement pattern. ∼ p ∧ [(p ∨ ∼ q) ∧ q]

Advertisements
Advertisements

प्रश्न

Construct the truth table of the following statement pattern.

∼ p ∧ [(p ∨ ∼ q) ∧ q]

सारिणी
Advertisements

उत्तर

p q ∼ p ∼ q p ∨ ∼ q (p ∨ ∼ q) ∧ q ∼ p ∧ [(p ∨ ∼ q) ∧ q]
T T F F T T F
T F F T T F F
F T T F F F F
F F T T T F 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 1.05 | 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 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


Using truth table prove that ∼p ˄ q ≡ (p ˅ q) ˄ ∼p


Using the truth table, prove the following logical equivalence :

p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)


Construct the truth table of the following statement pattern.

(∼ p → ∼ q) ∧ (∼ q → ∼ p)


Construct the truth table of the following:

∼ (∼p ∧ ∼q) ∨ q


Construct the truth table of the following:

[(p ∧ q) ∨ r] ∧ [∼r ∨ (p ∧ q)]


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

(p ∨ q) is T and (p ∨ q) → q is F


Express the following statement in symbolic form.

e is a vowel or 2 + 3 = 5


Express the following statement in symbolic form.

Mango is a fruit but potato is a vegetable.


Write the truth value of the following statement.

A quadratic equation has two distinct roots or 6 has three prime factors.


Write the negation of the following statement.

2 + 3 ≠ 5


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

For every x ∈ N, x + 3 < 8.


Write the following statement in symbolic form.

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


Write the following statement in symbolic form.

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


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) 


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.


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

If proof is lengthy then it is 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 ∨ 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.

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.


Rewrite the following statement without using the connective ‘If ... then’.

If a quadrilateral is rhombus then it is not a square.


Write the negation of the following statement.

I will have tea or coffee.


Write the negation of the following statement.

∀ n ∈ N, n + 3 > 9.


A biconditional statement is the conjunction of two ______ statements.


If p → q is an implication, then the implication ∼ q → ∼ p is called its


Write the following compound statements symbolically.

Triangle is equilateral or isosceles


Write the following statements in symbolic form

Even though it is not cloudy, it is still raining


Without using truth table show that -

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


State whether the following statement is True or False:

The converse of inverse of ~ p → q is q → ~ p


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


Given 'p' and 'q' as true and 'r' as false, the truth values of p v (q ∧ ~r) and (p → r) ∧ q are respectively


If p, q are true statement and r is false statement, then which of the following statements is a true statement.


If q: There are clouds in the sky then p: it is raining. The symbolic form is ______


The inverse of the statement "If its quality is good. then it is expensive.", is ______ 


The statement, 'If I go to school, then I will get knowledge' 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 ______


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


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


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.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×