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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.

User PawelP
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1 Answer

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Final answer:

Both statements are false. Statement 1 should say that a square has exactly four sides, and Statement 2 should clarify that a square must have four sides, not less. The two statements are different; one misdescribes a square's properties, and the other incorrectly defines what could be a square.

Step-by-step explanation:

The question asks us to evaluate two conditional statements related to the properties of geometric shapes and determine their truth value and whether they express the same meaning.

Statement 1 is false. The correct statement is: 'If it is a square, then it has exactly four sides.' A square is defined as a quadrilateral with four equal sides and four right angles. Therefore, a square cannot have more than four sides.

Statement 2 is also false. The correct statement is: 'If it has exactly four sides, then it might be a square.' Having less than four sides does not define a square; instead, a square must have four sides. A shape with less than four sides could be a triangle, but never a square.

Furthermore, these statements do not have the same meaning; one describes an incorrect property of a square, while the other incorrectly defines what may constitute a square based on the number of sides.

User Nitin Kabra
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