Read the following statements:

Statement 1: If it is a square, then it has more than four sides.
Statement 2: If it has less than four sides, then it is a square.

Determine if the statements are true or false and if they have the same meaning.

Both statements are true and they have the same meaning.
Both statements are false and they have the same meaning.
Both statements are true and they do not have the same meaning.
Both statements are false and they do not have the same meaning.

1 answer

Let's analyze the two statements one by one.

Statement 1: "If it is a square, then it has more than four sides."

This statement is false. A square has exactly four sides, not more than four.

Statement 2: "If it has less than four sides, then it is a square."

This statement is also false. A shape with less than four sides could be a triangle (which has three sides) or another polygon with even fewer sides, neither of which are squares.

Now let's consider the meanings of the two statements:

  • Statement 1 suggests that being a square implies having more than four sides, which is incorrect.
  • Statement 2 suggests that having fewer than four sides implies being a square, which is also incorrect.

Thus, both statements are false, and they clearly do not have the same meaning.

The correct conclusion is: Both statements are false and they do not have the same meaning.