Question

Is the conditional statement true? If not, find the counterexample. (1 point)

Answer 1

The correct answers are:

C) No, a counterexample is a pea; D) Points lie on the same line if and only if the points are collinear; and B) If a fruit is an apple, then it grows on a tree.

Explanation:

For the first question, broccoli is not the only green vegetable.  Peas are vegetables and are also green, so this would be a good counterexample.

For the second question, a biconditional is written as the first statement "if and only if" the second statement.  For the statement "Points that lie on the same line are collinear," the two conditionals would be "If points lie on the same line, they are collinear" and "If points are collinear, then they lie on the same line."  To write this in "if and only if" form, we write "Points lie on the same line if and only if the points are collinear."

For the third question, "Apples grow on trees" can be written as an "if-then" statement as "If a fruit is an apple, then it grows on a tree."

Answer 2

Is the conditional statement true? If not, find the counterexample. (1 point)

If a vegetable is green, then it is broccoli.

A. The statement is true

B. No a counterexample is a carrot.

C. No a counterexample is a pea

D. No a counterexample is a kiwi

ANSWER:

We know that not all vegetables are green so answer will be (B. No a counterexample is a carrot). Because carrot is not green.

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Rewrite the following definition as a bi-conditional: (1 point)

Points that lie on the same line are collinear.

A. If a point lies on a line, then it is collinear.

B. If a point lies on a line with another point, then the two points are collinear.

C. If two points are collinear, then they lie on the same line.

D. Points lies on the same line if and only if the points are collinear.

ANSWER:

Bi-conditional statemensts are written in form of "if and only if". Choice D) matches with that format and also means same thing as the given statement.

Hence (D. Points lies on the same line if and only if the points are collinear.) is the final answer.

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Rewrite the following statement as a conditional statement: (1 point)

Apples grow on trees.

A. If it grows on a tree, it is an apple.

B. If a fruit is an apple, then it grows on a tree.

C. Apples are a fruit if an only if they grow on a tree.

D. If it is not a fruit, then it is not an apple.

ANSWER:

Conditional statement is written in form of "if p then q". Now reading the given choices and comparing with real life situation, we will find that only choice B "If a fruit is an apple, then it grows on a tree." is correct.

As not all fruits growing on tree are apple so choice A is not possible. There are many fruits other than apple so choice D is also wrong. choice C not in form of If p then q so it is also wrong.