Truth Value/Counter Example
The difference of two even numbers is always an even number.
True
Scott leaves for school at 8:15 in the morning every day, it takes him 15 minutes to get to school, and he arrives on time. If Scott leaves at 8:15 this morning, he will arrive at school on time.
Deductive
Identify the hypothesis of the following statement:
If it is summer, then there are kids outside
If it is summer
What property is shown:
4x+3 = 6
4x = 3
Subtraction property
The sum of two acute angles is always acute
False, many options to check
On Monday, Sophie went to lunch at the local fast-food joint on her lunch break and arrived back at school in time for class. On Tuesday, she did the same thing and was on time again. If Sophie goes to the same fast-food place for lunch on every day, she will be back in time for class.
Inductive
Identify the conclusion of the following statement:
If it is summer, then there are kids outside
What property is shown:
4x+3 =y
y=4x+3
Symmetric Property
The product of two numbers is always greater than both numbers.
False, many examples
3(x-4)-7=6x therefore x=-6.333333
Deductive
Write the inverse to the following statement:
If it is summer, then there are kids outside
If it is not summer, then there are no kids outside.
Name the property
4x+3 = 23 x=5
4(5)+3=18
Substitution property
Five red candies are pulled out of a bag, all the candies in the bag are red.
False, candy could be any color
If y=5 and x=3 therefore y-2=x
Inductive reasoning, from specific stated values of x and y to a general statement about them both.
Write the converse of the following statement:
If it is summer, then there are kids outside
If there are kids outside, then it is summer.
5(x+3)=14
5x+15=14
Distributive property
If Points R, S, and Tare noncollinear, then segments RS, ST, and RT must form a triangle.
True
All housecats are felines. All felines have claws. Therefore all housecats have claws.
Deductive
Write the contrapositive of the following statement:
If it is summer, then there are kids outside
If there are no kids outside, then it is not summer.
Name the property
4x=4x
Reflexive property