Conditional Statements and Symbolic Representations

Given, "If I have a Siberian Husky, then I have a dog." Identify the converse.

• If I do not have a Siberian Husky, then I do not have a dog.
• If I have a dog, then I have a Siberian Husky.
• If I do not have a dog, then I do not have a Siberian Husky.
• If I do not have a Siberian Husky, then I have a dog. 

Original: If Emily is not late to class, then she will not be marked tardy.
What is this? If Emily is late to class, then she will be marked tardy.

• Converse
• Inverse
• Contrapositive
• Negation

Original: If Jenny buys a guitar, then she will not buy a keyboard.
What is this? If Jenny does buy a keyboard, then she will not buy a guitar.

• Converse
• Inverse
• Contrapositive
• Negation

What is the contrapositive to this?

• If the food is not cooked, then it is not in the oven.
• If the food is not in the oven, then it is not cooked.
• If the food is cooked, then its in the oven.
• If food is not in the oven, then its cooked.

Q. Given, "If I have a Siberian Husky, then I have a dog." Identify the contrapositive.

• If I do not have a Siberian Husky, then I do not have a dog.

• If I have a dog, then I have a Siberian Husky.

• If I do not have a dog, then I do not have a Siberian Husky.

• If I do not have a Siberian Husky, then I have a dog.

Consider the following statements.

p: two lines are parallel

q: corresponding angles are congruent

Which of the following is the symbolic representation of the statement,

If two lines are not parallel, then corresponding angles are not congruent.

• ∼p→∼q

• ∼q→∼p

• q→p

• p→q

Tags

CCSS.HSG.CO.C.9

CCSS.HSG.GPE.B.5

Let p represent “x² ≠ 64.”

Let q represent “x is not a rational number.” Which is a representation of the statement below?

If x is a rational number, then x² = 64.

• ∼p→∼q

• ∼p→q

• p→∼q

• ∼q→∼p

Tags

CCSS.HSS.CP.A.1

Consider the following statements represented by pand q:

p: The sum of two angles is 180°.

q: The two angles are supplements.

Which of the following is a symbolic representation of the statement

"If two angles are not supplements, then the sum of the two angles is not 180°."

• q→∼p

• p→∼q

• ∼q→∼p

• ∼p→∼q

Let s represent “eat your vegetables,” let r represent “eat your dessert,” and t represent “you can go to the party.” Which statement represents ∼r→t?

• If you eat your vegetables, then you can go to the party.

• If you eat your dessert, then you can to the party.

• If you do not eat your vegetables, then you cannot go the party.

• If you do not eat your dessert, then you can go to the party.

r:  it is raining
s: sidewalks are wet
Write "If it is not raining then the sidewalks are not wet in symbolic form.

• ∼r→∼s
• ∼s→r
• r→s
• s→r

Tags

CCSS.HSS.CP.A.1