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Hint: Use the definition of the contrapositive concept of mathematical logic and convert the given statement into the contrapositive statement.
Formula used:
The contrapositive of a conditional statement, interchange the original hypothesis and the conclusion of the statement.
The negation of a statement is the opposite of the original statement.
The negation is represented by a symbol: \[\sim \]
Complete step by step solution:
The given statement is “If two triangles are identical, then these are similar.”
Let’s consider,
\[p:\] two triangles are identical
\[q:\] two triangles are similar
So, the symbolic representation of the given statement is: \[p \to q\]
Now apply the definition of the contrapositive concept of mathematical logic.
Then the contrapositive representation is: \[\sim q \to \sim p\]
The negation statements of the above statements are:
\[\sim p :\] two triangles are not similar
\[\sim q :\] two triangles are not identical
Therefore, the word representation of the contrapositive statement is,
\[\sim q \to \sim p\]: If two triangles are not similar, then these are not identical.
Hence the correct option is A.
Note: Students often get confused and consider contrapositive as the negation.
A contrapositive statement is a negation of terms of a converse statement.
Statement: \[a \to b\]
Contrapositive statement: \[\sim b \to \sim a\]
Formula used:
The contrapositive of a conditional statement, interchange the original hypothesis and the conclusion of the statement.
The negation of a statement is the opposite of the original statement.
The negation is represented by a symbol: \[\sim \]
Complete step by step solution:
The given statement is “If two triangles are identical, then these are similar.”
Let’s consider,
\[p:\] two triangles are identical
\[q:\] two triangles are similar
So, the symbolic representation of the given statement is: \[p \to q\]
Now apply the definition of the contrapositive concept of mathematical logic.
Then the contrapositive representation is: \[\sim q \to \sim p\]
The negation statements of the above statements are:
\[\sim p :\] two triangles are not similar
\[\sim q :\] two triangles are not identical
Therefore, the word representation of the contrapositive statement is,
\[\sim q \to \sim p\]: If two triangles are not similar, then these are not identical.
Hence the correct option is A.
Note: Students often get confused and consider contrapositive as the negation.
A contrapositive statement is a negation of terms of a converse statement.
Statement: \[a \to b\]
Contrapositive statement: \[\sim b \to \sim a\]
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