Learning Task 3 A. Write each sentence as:
(a) Conditional Statement
(c) Inverse Statement
(b) Converse Statement
(d) Contrapositive Statement
1. Vegetables are good for your health.
2. 3x + 8 = 14, x = 2
3. A right triangle has a 90° angle.
4. An eagle is a bird.
5. A whale is a mammal.
6. Two circle with equal diameters are congruent.
7. An angle that measures between 90 and 180 degrees is obtuse
angle.
8. Two planes with no common point are parallel.
9. Carrot is rich in Vitamin A.
10. All reptiles have scales.
B. Determine which statements in A both the conditional and converse
statements are true. Write it in biconditional statement.

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A)

1.

Statement is - Vegetables are good for your health.

Let P - There are Vegetables , Q - they are good for health

Conditional statement is -If there are Vegetables , then they are good for the health.

Inverse Statement is - If there are no Vegetables, then they are not good for health.

Converse statement - If they are good for health , then they are vegetables.

Contra-positive statement - If they are not good for health , then they are not vegetables.

2.

Statement is - 3x + 8 = 14, x = 2

Let P - 3x + 8 = 14 , Q - x = 2

Conditional statement is -If 3x + 8 = 14 , then x = 2.

Inverse Statement is - If 3x + 8 ≠ 14 , then x ≠ 2.

Converse statement - If x = 2 , then 3x + 8 = 14

Contra-positive statement - If x ≠ 2 , then 3x + 8 ≠ 14

3.

Statement is - A right triangle has a 90° angle.

Let P - Triangle has a 90° angle , Q - It is right triangle .

Conditional statement is -If Triangle has a 90° angle , then It is right triangle.

Inverse Statement is - If Triangle has not a 90° angle , then It is not right triangle.

Converse statement - If It is right triangle , then Triangle has a 90° angle.

Contra-positive statement - If It is not a right triangle  , then Triangle has not a 90° angle.

4.

Statement is - An eagle is a bird .

Let P - It is an eagle  , Q - It is a bird

Conditional Statement - If it is an eagle , then it is a bird.

Inverse statement - If it is not eagle , then it is not bird.

Converse statement - If it is a bird , then it is an eagle.

Contra-positive statement - If it is not a bird , then it is not an eagle.

5.

Statement is - A whale is a mammal

Let  P - It is a whale , Q - It is a mammal

Conditional Statement - If it is a whale , then it is a mammal.

Inverse statement - If it is not whale , then it is not mammal.

Converse statement - If it is a mammal , then it is a whale.

Contra-positive statement - If it is not a mammal , then it is not a whale.

6.

Statement is - Two circle with equal diameters are congruent

Let  P - Two circles have equal diameters , Q - They are congruent

Conditional Statement - If Two circles have equal diameters , then they are congruent.

Inverse statement - If two circles have not equal diameters , then they are not congruent.

Converse statement - If two circles are congruent , then they have equal diameters.

Contra-positive statement - If two circles are not congruent , then they have not equal diameters.

7.

Statement is - An angle that measures between 90 and 180 degrees is obtuse  angle

Let  P - An angle that measures between 90 and 180 degrees , Q - They are obtuse angle.

Conditional Statement - If An angle that measures between 90 and 180 degrees , then they are obtuse angle.

Inverse statement - If An angle that does not measures between 90 and 180 degrees , then they are not obtuse angle.

Converse statement - If an angle is obtuse angle , then that angle measures between 90 and 180 degrees.

Contra-positive statement - If an angle is not an obtuse angle , then that angle does not measures between 90 and 180 degrees.

8.

Statement is - Two planes with no common point are parallel.

Let P - Two planes have no common point , Q - they are parallel.

Conditional Statement - If Two planes have no common point , then they are parallel.

Inverse statement - If two planes have common point , then they are not parallel.

Converse statement - If two planes are parallel, then they have no common point.

Contra-positive statement - If two planes are not parallel, then they have common point.

9.

Statement is - Carrot is rich in Vitamin A.

Let P -  There are carrots , Q - they are rich in Vitamin A

Conditional statement is -If There are carrots , then they are rich in Vitamin A.

Inverse Statement is - If there are no carrots , then they are not rich in Vitamin A.

Converse statement - If they are rich in Vitamin A , then they are carrots

Contra-positive statement - If they are not rich in Vitamin A , then they are not carrots.

10.

Statement is - All reptiles have scales.

Let  P - All are reptiles , Q - they all have scales.

Conditional statement - If all are reptiles , then they all have scales.

Inverse statement - If all are not reptiles , they have no scales.

Converse statement - If all have scales , then all are reptiles.

Contra-positive statement - If all have no scales , then they all are not reptiles.

B)

1. Both the conditional and converse  statements are true.

Bi-conditional statement - There are vegetables if and only if they are good in health.

3. Both the conditional and converse  statements are true.

Bi-conditional statement - A triangle has a 90° angle if and only if it is a right triangle.

6. Both the conditional and converse  statements are true.

Bi-conditional statement - Two circle are equal diameter if and only if they are congruent.

7. Both the conditional and converse  statements are true.

Bi-conditional statement - An angle that measures between 90 and 180 degrees if and only if it is an  obtuse  angle.

8. Both the conditional and converse  statements are true.

Bi-conditional statement - Two planes has no common point if and only if they are parallel.

answer: 2 and 1

step-by-step explanation: got this question

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