Question

if 47% of the dogs at the shelter are female, then 53% of the dogs are male. can he rewrite this as a true biconditional? explain. see example 6
write two conditionals from each biconditional. see example 7

1. a month has exactly 28 days if and only if it is february.
2. two angles are complementary if and only if their measures add up to 90.
3. the area of a square is s² if and only if the perimeter of the square is 4s.

Explanation:

A biconditional statement "p if and only if q" can be written as two conditional statements: "if p then q" and "if q then p".
For 30:

• Conditional 1: If a month has exactly 28 days, then it is February.
• Conditional 2: If it is February, then the month has exactly 28 days (ignoring leap - years for simplicity).

For 31:

• Conditional 1: If two angles are complementary, then their measures add up to 90.
• Conditional 2: If the measures of two angles add up to 90, then the two angles are complementary.

For 32:

• Conditional 1: If the area of a square is \(s^{2}\), then the perimeter of the square is \(4s\).
• Conditional 2: If the perimeter of the square is \(4s\), then the area of a square is \(s^{2}\).

Answer:

30.
If a month has exactly 28 days, then it is February.
If it is February, then the month has exactly 28 days.
31.
If two angles are complementary, then their measures add up to 90.
If the measures of two angles add up to 90, then the two angles are complementary.
32.
If the area of a square is \(s^{2}\), then the perimeter of the square is \(4s\).
If the perimeter of the square is \(4s\), then the area of a square is \(s^{2}\).