English

Write Converse and Inverse of the Following Statement : If Ravi is Good in Logic Then Ravi is Good in Mathematics - Mathematics and Statistics

Advertisements
Advertisements

Question

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

Sum

Solution

Let p : Ravi is good in Logic.
      q : Ravi is good in Mathematics.
       Given statement is p → q
       Converse : q → P
If Ravi is good in Mathematics then he is good in Logic.
Inverse : ∼ p → ∼ q
If Ravi is not good in Logic then he is not good in Mathematics.

shaalaa.com
  Is there an error in this question or solution?
2015-2016 (March)

APPEARS IN

RELATED QUESTIONS

Express the following statement in symbolic form and write its truth value.

"If 4 is an odd number, then 6 is divisible by 3 "


Write converse and inverse of the following statement: 
“If a man is a bachelor then he is unhappy.” 


Use the quantifiers to convert the following open sentence defined on N into true statement
5x - 3 < 10


Prove that the following statement pattern is equivalent:
(p v q) → r and (p → r) ∧ (q → r)


Write the negation of the Following Statement :
∀ y ∈  N, y2 + 3 ≤ 7


State if the following sentence is a statement. In case of a statement, write down the truth value :
Every quadratic equation has only real roots.


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


Using the truth table prove the following logical equivalence.

∼ (p ∨ q) ∨ (∼ p ∧ q) ≡ ∼ p


Using the truth table prove the following logical equivalence.

p ↔ q ≡ ∼ [(p ∨ q) ∧ ∼ (p ∧ q)]


Using the truth table prove the following logical equivalence.

p → (q → p) ≡ ∼ p → (p → q)


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

[(p → q) ∧ ∼ q] → ∼ p


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

[p → (∼ q ∨ r)] ↔ ∼ [p → (q → r)]


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)] ∧ r


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

(p ∧ ~ q) → (~ p ∧ ~ q)


If p is any statement then (p ∨ ∼p) is a ______.


Prove that the following statement pattern is a contradiction.

(p → q) ∧ (p ∧ ~ q)


Fill in the blanks :

Inverse of statement pattern p ↔ q is given by –––––––––.


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


Prove that the following pair of statement pattern is equivalent.

~(p ∧ q) and ~p ∨ ~q


Write the negation of the following statement.

Some continuous functions are differentiable.


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

(~p ∧ q) ∧ (~q ∨ ~r)


With proper justification, state the negation of the following.

(p ↔ q) v (~ q → ~ r)


Construct the truth table for the following statement pattern.

(p ∧ ~ q) ↔ (q → p)


What is tautology? What is contradiction?
Show that the negation of a tautology is a contradiction and the negation of a contradiction is a tautology.


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

[~(p ∨ q) → p] ↔ [(~p) ∧ (~q)]


Using the truth table, prove the following logical equivalence.

p ∧ (~p ∨ q) ≡ p ∧ q


Write the dual of the following.

(p ∧ q) ∧ r ≡ p ∧ (q ∧ r)


The contrapositive of p → ~ q is ______


If p → (∼p v q) is false, then the truth values of p and q are respectively


If p → q is true and p ∧ q is false, then the truth value of ∼p ∨ q is ______


The converse of contrapositive of ∼p → q is ______.


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×