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Choose the correct alternative: Which one of the following is not true? - Mathematics

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प्रश्न

Choose the correct alternative:

Which one of the following is not true?

पर्याय

  • Negation of a statement is the statement itself

  • If the last column of the truth table contains only T then it is a tautology

  • If the last column of its truth table contains only F then it is a contradiction

  • If p and q are any two statements then p ⟷ q is a tautology

MCQ

उत्तर

If p and q are any two statements then p ⟷ q is a tautology

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Mathematical Logic
  या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?
पाठ 12: Discrete Mathematics - Exercise 12.3 [पृष्ठ २५१]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 12 TN Board
पाठ 12 Discrete Mathematics
Exercise 12.3 | Q 20 | पृष्ठ २५१

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


Write the following sentences in symbolic form using statement variables p and q.

19 is not a prime number and all the angles of a triangle are equal


Write the following sentences in symbolic form using statement variables p and q.

19 is a prime number and all the angles of a triangle are equal


Write the following sentences in symbolic form using statement variables p and q.

19 is not a prime number


Determine the truth value of the following statement.

If 6 + 2 = 5, then the milk is white.


Determine the truth value of the following statement.

It is not true that 5 + 5 = 9 or Earth is a planet


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

If a quadrilateral is a square then it is a rectangle


Construct the truth table for the following statement.

¬(P ∧ ¬q)


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

((p v q) ∧¬p) → q


Prove that q → p ≡ ¬p → ¬q


Using the truth table check whether the statements ¬(p v q) v (¬p ∧ q) and ¬p are logically equivalent


Prove p → (q → r) ≡ (p ∧ q) → r without using the truth table


Choose the correct alternative:

The operation * defined by a * b = `"ab"/7` is not a binary operation on


Choose the correct alternative:

Which one of the following statements has the truth value T?


Choose the correct alternative:

Which one of the following statements has truth value F?


Choose the correct alternative:

The truth table for (p ∧ q) v ¬q is given below

p q (p ∧ q) v ¬q
T T (a)
T F (b)
F T (c)
F F (d)

Which one of the following is true?


Choose the correct alternative:

Which one of the following is incorrect? For any two propositions p and q, we have


Choose the correct alternative:

p q (p ∧ q) → ¬p
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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