Match the following : Codes :List – I List – II a. Absurd i. Clearly impossible being contrary to some evident truth. b. Ambiguous ii. Capable of more than one interpretation or meaning. c. Axiom iii. An assertion that is accepted and used without a proof. d. Conjecture iv. An opinion preferably based on some experience or wisdom.
a-i, b-ii, c-iii, d-iv
The four terms belong to the vocabulary of mathematical reasoning; each is matched by its standard dictionary and logic-text meaning.
a. Absurd — a statement is absurd when it is clearly impossible because it contradicts an evident truth; reductio ad absurdum proofs rely on reaching exactly such a contradiction. So a → i.
b. Ambiguous — an expression is ambiguous when it admits more than one interpretation or meaning (for example, an ambiguous grammar gives a sentence two parse trees). So b → ii.
c. Axiom — an axiom is an assertion accepted and used without proof, serving as a starting point for deductions. So c → iii.
d. Conjecture — a conjecture is an opinion or proposition put forward on the basis of experience or partial evidence but not yet proved. So d → iv.
The other code rows pair Absurd with “more than one interpretation”, Axiom with an opinion based on experience, or Conjecture with impossibility, each of which contradicts the definitions above.
a-i, b-ii, c-iii, d-iv option is correct.
Similar Questions
Match the following terms :
List - I List - II (a) Vacuous proof (i) A proof that the implication \(p \rightarrow q\) is true based on the fact that p is false. (b) Trivial proof (ii) A proof that the implication \(p \rightarrow q\) is true based on the fact that q is true. (c) Direct proof (iii) A proof that the implication \(p \rightarrow q\) is true that proceeds by showing that q must be true when p is true. (d) Indirect proof (iv) A proof that the implication \(p \rightarrow q\) is true that proceeds by showing that p must be false when q is false. Codes :
Which one of the following is true ?
Consider a proposition given as :
“ \(x \geq 6\), if \(x^{2} \geq 25\) and its proof as :
If \(x \geq 6\), then \(x^{2} = x \cdot x \geq 6 \cdot 6 = 36 \geq 25\)
Which of the following is correct w.r.to the given proposition and its proof ?
(a) The proof shows the converse of what is to be proved.
(b) The proof starts by assuming what is to be shown.
(c) The proof is correct and there is nothing wrong.
The mathematical notation to describe logical entailment of a scentence “α entails another sentence β” is
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Which of the following equation represents a function?
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- \(\sqrt[3]{{\sqrt {0.000729} }} =\)
