मराठी
महाराष्ट्र राज्य शिक्षण मंडळएचएससी वाणिज्य (इंग्रजी माध्यम) इयत्ता १२ वी

Prove that the following statement pattern is a contradiction. (p ∧ q) ∧ ~p - Mathematics and Statistics

Advertisements
Advertisements

प्रश्न

Prove that the following statement pattern is a contradiction.

(p ∧ q) ∧ ~p

बेरीज
Advertisements

उत्तर

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

All the truth values in the last column are F. Hence, it is a contradiction.

shaalaa.com
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 1: Mathematical Logic - Exercise 1.6 [पृष्ठ १६]

APPEARS IN

बालभारती Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
पाठ 1 Mathematical Logic
Exercise 1.6 | Q 4.2 | पृष्ठ १६

संबंधित प्रश्‍न

If p and q are true statements and r and s are false statements, find the truth value of the following :
( p ∧  ∼ r ) ∧ ( ∼ q ∧ s )


If   p : It is raining
     q : It is humid

Write the following statements in symbolic form:

(a) It is raining or humid.
(b) If it is raining then it is humid.
(c) It is raining but not humid. 


State if the following sentence is a statement. In case of a statement, write down the truth value :
√-4 is a rational number.


Write converse and inverse of the following statement :
"If Ravi is good in logic then Ravi is good in Mathematics."


By constructing the truth table, determine whether the following statement pattern ls a tautology , contradiction or . contingency.  (p →  q) ∧  (p ∧ ~ q ).


Using the truth table prove the following logical equivalence.

p → (q → p) ≡ ∼ p → (p → q)


Using the truth table prove the following logical equivalence.

p → (q ∧ r) ≡ (p → q) ∧ (p → r)


Examine whether the following statement pattern is a tautology or a contradiction or a contingency.

[(p → q) ∧ ∼ q] → ∼ p


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


Determine whether the following statement pattern is a tautology, contradiction or contingency:

[p → (q → r)] ↔ [(p ∧ q) → r]


Determine whether the following statement pattern is a tautology, contradiction or contingency:

[(p ∨ ∼q) ∨ (∼p ∧ q)] ∧ r


Prove that the following statement pattern is a tautology.

(p → q) ↔ (~ q → ~ p)


Prove that the following statement pattern is a contradiction.

(p ∨ q) ∧ (~p ∧ ~q)


Prove that the following statement pattern is a contradiction.

(p ∧ q) ∧ (~p ∨ ~q)


Show that the following statement pattern is contingency.

(p → q) ↔ (~ p ∨ q)


Show that the following statement pattern is contingency.

p ∧ [(p → ~ q) → q]


Show that the following statement pattern is contingency.

(p → q) ∧ (p → r)


Using the truth table, verify.

p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)


Prove that the following pair of statement pattern is equivalent.

p → q and ~ q → ~ p and ~ p ∨ q


Using the rules of negation, write the negation of the following:

(~p ∧ q) ∧ (~q ∨ ~r)


Using the truth table, prove the following logical equivalence.

[~(p ∨ q) ∨ (p ∨ q)] ∧ r ≡ r


State the dual of the following statement by applying the principle of duality.

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


The false statement in the following is ______.


Write the dual of the following.

13 is prime number and India is a democratic country


Determine whether the following statement pattern is a tautology, contradiction, or contingency:

[(∼ p ∧ q) ∧ (q ∧ r)] ∧ (∼ q)


Examine whether the following statement pattern is a tautology or a contradiction or a contingency:

(∼p ∧ ∼q) → (p → q)


Prepare truth table for the statement pattern `(p -> q) ∨ (q -> p)` and show that it is a tautology.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×