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Show that p → q and q → p are not equivalent - Mathematics

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प्रश्न

Show that p → q and q → p are not equivalent

सारिणी
योग
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उत्तर

p q p → q q → p
T T T T
T F F T
F T T F
F F T T

From the table, it is clear that

p → q ≠ q → P

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Mathematical Logic
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 12: Discrete Mathematics - Exercise 12.2 [पृष्ठ २४९]

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सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
अध्याय 12 Discrete Mathematics
Exercise 12.2 | Q 10 | पृष्ठ २४९

संबंधित प्रश्न

Let p : Jupiter is a planet and q : India is an island be any two simple statements. Give verbal sentence describing the following statement.

p ↔ q


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Which one of the following sentences is a proposition?

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Which one of the following sentences is a proposition?

Peacock is our national bird


Which one of the following sentences is a proposition?

How tall this mountain is!


Write the converse, inverse, and contrapositive of the following implication.

If x and y are numbers such that x = y, then x2 = y2


Construct the truth table for the following statement.

(p v q) v ¬q


Construct the truth table for the following statement

(¬p → r) ∧ (p ↔ q)


Verify whether the following compound propositions are tautologies or contradictions or contingency.

((p v q) ∧¬p) → q


Verify whether the following compound propositions are tautologies or contradictions or contingency.

(p → q) ↔ (¬p → q)


Prove that p → (¬q v r) ≡ ¬p v (¬q v r) using truth table


Choose the correct alternative:

If a compound statement involves 3 simple statements, then the number of rows in the truth table is


Choose the correct alternative:

Which one is the inverse of the statement (p v q) → (p ∧ q)?


Choose the correct alternative:

Which one is the contrapositive of the statement (p v q) → r?


Choose the correct alternative:

In the last column of the truth table for ¬(p v ¬q) the number of final outcomes of the truth value ‘F’ is


Choose the correct alternative:

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T T (a)
T F (b)
F T (c)
F F (d)

Which one of the following is correct for the truth value of (p ∧ q) → ¬p


Choose the correct alternative:

The proposition p∧(¬p∨q)] is


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