Question

1-1b practice worksheet - conditional statements
statement example
conditional if a figure is a square, then it has four right angles.
converse: switch h and c. if a figure has four right angles, then it is a square.
show that each conditional is false by finding a counter - example.

1. if it is 12:00 noon, then the sun is shining.
2. if a number is divisible by 3, then it is odd.

write the converse of each conditional.

1. if you drink milk, then you will be strong.
2. if a rectangle has four sides the same length, then it is a square.
3. if a rectangle has four sides the same length, then it is a square.
4. if you do not sleep, you will be tired.

write the converse and decide whether the converse is true or false. if the converse is false, give a counter - example.

1. if the sun is shining, then it is 12:00 noon.
2. if the number is divisible by 3, then the number is odd.
3. if an angle is 90°, then it is a right angle.

Explanation:

Step1: Find counter - example for "If it is 12:00 noon, then the sun is shining"

It can be 12:00 noon on a cloudy or rainy day. So a counter - example is a 12:00 noon with overcast skies.

Step2: Find counter - example for "If a number is divisible by 3, then it is odd"

The number 6 is divisible by 3 but is even. So 6 is a counter - example.

Step3: Write the converse of "If you drink milk, then you will be strong"

Switch the hypothesis and conclusion. The converse is "If you are strong, then you drink milk."

Step4: Write the converse of "If a rectangle has four sides the same length, then it is a square"

The converse is "If a figure is a square, then it is a rectangle with four sides the same length."

Step5: (Same as Step 4 as it's the same statement repeated)

The converse is "If a figure is a square, then it is a rectangle with four sides the same length."

Step6: Write the converse of "If you do not sleep, you will be tired"

Switch the hypothesis and conclusion. The converse is "If you are tired, then you did not sleep."

Step7: Write the converse of "If the sun is shining, then it is 12:00 noon" and check its truth

The converse is "If it is 12:00 noon, then the sun is shining". It is false. A counter - example is a 12:00 noon on a cloudy day.

Step8: Write the converse of "If the number is divisible by 3, then the number is odd" and check its truth

The converse is "If a number is odd, then it is divisible by 3". It is false. A counter - example is the number 5 (it is odd but not divisible by 3).

Step9: Write the converse of "If an angle is 90°, then it is a right angle" and check its truth

The converse is "If an angle is a right angle, then it is 90°". It is true.

Answer:

1. Counter - example: 12:00 noon on a cloudy day.
2. Counter - example: 6.
3. Converse: If you are strong, then you drink milk.
4. Converse: If a figure is a square, then it is a rectangle with four sides the same length.
5. Converse: If a figure is a square, then it is a rectangle with four sides the same length.
6. Converse: If you are tired, then you did not sleep.
7. Converse: If it is 12:00 noon, then the sun is shining. False. Counter - example: 12:00 noon on a cloudy day.
8. Converse: If a number is odd, then it is divisible by 3. False. Counter - example: 5.
9. Converse: If an angle is a right angle, then it is 90°. True.