Question

Which statement is logically equivalent to the following conditional statement?

If it is a rectangle, then it does not have three sides.

If it has three sides, then it is not a rectangle.

If it is not a rectangle, then it has three sides.

If it does not have three sides, then it is a rectangle.

If it is not a rectangle, then it does not have three sides.



What is the disjunction of the following two statements?

Statement 1: Pizza is good for you.
Statement 2: The sky is blue.

Pizza is good for you, and the sky is blue.

Pizza is

Answer 1

@satellite73 @Hero @Directrix @seesawn @Frostbite @Kainui

Answer 2

@Goten77

Answer 3

first Q, which statement means the same as the original?

Answer 4

well i would guess the 1st 1 was ur statement so the 1 after that would b the only1 to really gramatically and logicall match up

Answer 5

Okay!

Answer 6

just number 1 i didnt mean to post the one about pizza

Answer 7

well actually im not sure now.. cause a rectangle does have atleast 3 sides... we kno it has 4 but saying it has 3 isnt exactly wrong ina a sense

Answer 8

but its the only1 to really make any sense with teh 1st statement

Answer 9

it would be 2nd statement

Answer 10

thank youuuu

Answer 11

What is the converse of the following statement?

“If his shoes are clean, then he did not walk in the mud.”

If his shoes are not clean, then he walked in the mud.

If his shoes are clean, then he walked in the mud.

If he walked in the mud, then his shoes are not clean.

If he did not walk in the mud, then his shoes are clean. @seesawn

Answer 12

do you know what a converse statement?

Answer 13

@lilmac123

A conditional and its contrapositive are logically equivalent.

>> it would be 2nd statement NOT correct because it is not the contrapositive of the given statement.

Answer 14

@lilmac123, it would be the third statement

Answer 15

Check out how to write the converse, contrapositive, and inverse of a given statement.

Answer 16

>> it would be the third statement
Not correct. The third statement is not the contrapositive of the given statement.

Answer 17

Jordan wrote the following steps to simplify the expression: 5x – (3x + 2 + 4x).

Step

Mathematical Statement

Justification

0

5x – (3x + 2 + 4x)

Given

1

5x – (3x + 4x + 2)



Associative Property of Addition

2

5x – (7x + 2)

Combine Like Terms

3

5x – 7x – 2

Distributive Property

4

(5x – 7x) – 2

Associative Property of Addition

5

–2x – 2

Combine Like Terms


Which step of justification is incorrect, and what should the justification for that step be to simplify the expression?
Step 3; Associative Property of Multiplication

Step 4; Commutative Property of Multiplication

Step 2; Associative Property of Addition

Step 1; Commutative Property of Addition