English

Write the following statement in symbolic form. Milk is white if and only if the sky is not blue.

Advertisements
Advertisements

Question

Write the following statement in symbolic form.

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

Sum
Advertisements

Solution

Let p: Milk is white.

q: Sky is blue.

The symbolic form is p ↔ ~ q.

shaalaa.com
  Is there an error in this question or solution?
Chapter 1.1: Mathematical Logic - Q.4

Video TutorialsVIEW ALL [2]

RELATED QUESTIONS

Using the truth table, prove the following logical equivalence :

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.

Nagpur is in Maharashtra and Chennai is in Tamil Nadu. 


Write the following compound statement symbolically. 

Hima Das wins gold medal if and only if she runs fast.


Write the negation of the following statement.

All men are animals.


Write the negation of the following statement.

− 3 is a natural number.


Write the negation of the following statement.

2 + 3 ≠ 5


Write the following statement in symbolic form.

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


Find the truth value of the following statement.

Neither 27 is a prime number nor divisible by 4.


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.

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.

The necessary condition for existence of a tangent to the curve of the function is continuity.


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


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.


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

If it rains then the principal declares a holiday.


Write the negation of the following statement.

10 > 5 and 3 < 8


Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”


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


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


The Boolean expression ∼(p ∨ q) ∨ (∼p ∧ q) 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? 


Write the converse, inverse, and contrapositive of the statement. "If 2 + 5 = 10, then 4 + 10 = 20."


Express the following compound statement symbolically:

3 + 8 ≥ 12 if and only if 5 × 4 ≤ 25


Using truth table prove that:

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


Construct the truth table for the statement pattern:

[(p → q) ∧ q] → p


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×