Question:
The contrapositive of "If two triangles are identical, then these are similar" is
The contrapositive of "If two triangles are identical, then these are similar" is
Updated On: May 17, 2024
- If two triangles are not similar then these are not identical
- If two triangles are not identical then these are not similar
- If two triangles are not identical then these are similar.
- If two triangles are not similar then these are identical.
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The Correct Option is A
Approach Solution - 1
Consider the following statements
$p:$ Two triangles are identical
$q:$ Two triangles are similar
Clearly, the given statement in symbolic form is $p \rightarrow q$
$\therefore$ Its contrapositive is given by
$\sim q \rightarrow \sim p$
Now, $\sim p$ : Two triangles are not identical $\sim q:$ Two triangles are not similar
$\therefore \sim q \rightarrow \sim p:$ If two triangles are not similar, then these are not identical
$p:$ Two triangles are identical
$q:$ Two triangles are similar
Clearly, the given statement in symbolic form is $p \rightarrow q$
$\therefore$ Its contrapositive is given by
$\sim q \rightarrow \sim p$
Now, $\sim p$ : Two triangles are not identical $\sim q:$ Two triangles are not similar
$\therefore \sim q \rightarrow \sim p:$ If two triangles are not similar, then these are not identical
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Approach Solution -2
Suppose p: Two triangles are the same.
q: Two triangles resemble one another
The above sentence is obviously pq in symbolic form. Its opposite is provided by qp.
i.e., Two triangles are not identical if they do not resemble one another.
q: Two triangles resemble one another
The above sentence is obviously pq in symbolic form. Its opposite is provided by qp.
i.e., Two triangles are not identical if they do not resemble one another.
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Concepts Used:
Mathematical Reasoning
Mathematical reasoning or the principle of mathematical reasoning is a part of mathematics where we decide the truth values of the given statements. These reasoning statements are common in most competitive exams like JEE and the questions are extremely easy and fun to solve.
Types of Reasoning in Maths:
Mathematically, reasoning can be of two major types such as:
- Inductive Reasoning - In this, method of mathematical reasoning, the validity of the statement is examined or checked by a certain set of rules, and then it is generalized. The principle of mathematical induction utilizes the concept of inductive reasoning.
- Deductive Reasoning - The principle is the opposite of the principle of induction. Contrary to inductive reasoning, in deductive reasoning, we apply the rules of a general case to a provided statement and make it true for particular statements. The principle of mathematical induction utilizes the concept of deductive reasoning.