English

Assuming the first statement p and second as q. Write the following statement in symbolic form. If the question paper is not easy then we shall not pass. - Mathematics and Statistics

Advertisements
Advertisements

Question

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

If the question paper is not easy then we shall not pass.

Sum

Solution

Let p : The question paper is not easy.
q : We shall not pass.

The symbolic form is p → q.

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] 12 Standard HSC Maharashtra State Board
Chapter 1 Mathematical Logic
Miscellaneous Exercise 1 | Q 4.03 | Page 32

RELATED QUESTIONS

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


Write converse, inverse contrapositive of the statement "If two triangles are not congruent then their areas are not equal.


Write the following compound statement symbolically.

Angle is neither acute nor obtuse.


Construct the truth table of the following statement pattern.

(p ∧ q) ↔ (q ∨ r)


Construct the truth table of the following statement pattern.

∼ p ∧ [(p ∨ ∼ q) ∧ q]


Construct the truth table of the following:

∼ (∼p ∧ ∼q) ∨ q


Write the truth value of the following statement.

Earth is a planet and Moon is a star.


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 following statement in symbolic form.

Stock prices are high if and only if stocks are rising.


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 : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

p ↔ ~ q


If p : He swims

q : Water is warm

Give the verbal statement for the following symbolic statement.

q ∧ ~ p


State whether the following statement is True or False:

The negation of 10 + 20 = 30 is, it is false that 10 + 20 ≠ 30.


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.


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

If a real number is not rational, then it must be irrational.


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


Rewrite the following statement without using conditional –
(Hint : p → q ≡ ∼ p ∨ q)

If demand falls, then price does not increase.


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

If 10 − 3 = 7 then 10 × 3 ≠ 30.


Consider the following statements.

  1. If D is dog, then D is very good.
  2. If D is very good, then D is dog.
  3. If D is not very good, then D is not a dog.
  4. If D is not a dog, then D is not very good. 

Identify the pairs of statements having the same meaning. Justify.


Write the negation of the following statement.

7 is prime number and Tajmahal is in Agra.


Write the negation of the following statement.

10 > 5 and 3 < 8


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


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


Write the following statements in symbolic form

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


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


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 ______


If c denotes the contradiction then the dual of the compound statement ∼p ∧ (q ∨ c) is ______ 


Which of the following is false?


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


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: ______ 


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×