English

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.

Advertisements
Advertisements

Question

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.

Sum
Advertisements

Solution

The symbolic form of the given statement is (p ∨ ~q) ↔ q.

∴ (p ∨ ~q) ↔ q ≡ (T ∨ ~T) ↔ T

≡ (T ∨ F) ↔ T

≡ T ↔ T

≡ T

Hence, truth value is T.

shaalaa.com
  Is there an error in this question or solution?
Chapter 1: Mathematical Logic - Miscellaneous Exercise 1 [Page 32]

APPEARS IN

Balbharati Mathematics and Statistics 1 (Commerce) [English] Standard 12 Maharashtra State Board
Chapter 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.07 | Page 32

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

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

[~(~p ∧ ~q)] v q


Using truth table, prove that ~ p ∧ q ≡ (p ∨ q) ∧ ~ p


Write the following compound statement symbolically.

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


Express the following statement in symbolic form.

Milk is white or grass is green.


Express the following statement in symbolic form.

Even though it is cloudy, it is still raining.


Write the truth value of the following statement.

The Himalayas are the highest mountains but they are part of India in the North East.


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.

If Kutub-Minar is in Delhi then Taj-Mahal is in Agra.


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.


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.

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.

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.

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 → 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


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.

If ∆ABC is not equilateral, then it is not equiangular.


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

If it rains then the principal declares a holiday.


Write the following statement in symbolic form:

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


Write the negation of p → q


Choose the correct alternative:

A biconditional statement is the conjunction of two ______ statements


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


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


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


Express the following compound statement symbolically:

3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25


Write the contrapositive of the inverse of the statement:

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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×