Logical Reasoning

Which is the converse of:
"If a figure is a circle with radius r, then its circumference in 2(pi)r."

• If a figure has a circumference of 2(pi)r, then its a circle with radius r.
• If a figure doesn't have a circumference, then it's a circle with a radius of r.
• If a figure isn't a circle with radius r, then its circumference isn't 2(pi)r
• If a figure isn't a circle, then it doesn't have a circumference.

Tags

CCSS.7.G.B.4

Contrapositive of:
If an integer ends with 0, then it's divisible by 2.

• If an integer ends with 2 then it's divisible by 0.
• If an integer doesn't end in 0, then it's not divisible by 2.
• If an integer isn't divisible by 2, then it's doesn't end in 0.
• If an integer is divisible by 2, then it ends with 0.

Inverse of: 
If you win the championship game, then you win the league trophy.

• If you don't win the championship game, then you don't win the league trophy.
• If you win the league trophy, then you win the championship game.
• If you don't win the league trophy, then you don't win the championship game.
• If you don't play the game, you can't win a trophy.

Which conclusion can you make?
If a whole number ends in 0, then it is divisible by 10. 
If a whole number is divisible by 10, then it is divisible by 5.

• If a whole number ends in 10 then it's divisible by 0.
• If a whole number ends in 5, then it's divisible by 10.
• If a whole number ends in 0, then it's divisible by 5.
• No conclusion can be made.

Tags

CCSS.4.OA.B.4

Which statement is a valid conclusion?
If a student has a temperature of 100 or more, then he/she should stay home from school. 
Jake has a temperature of 101 and Suzi has a temperature of 99.

• Both Jake and Suzi should stay home.
• Both should go see the school nurse.
• Jake should stay home, but Suzi should go to school.
• Suzi should stay home, but Jake should go to school.

Tags

CCSS.RI.11-12.2

CCSS.RI.8.1

CCSS.RI.9-10.1

CCSS.RL.11-12.1

CCSS.RL.9-10.1

Make a valid conclusion:
If a blub is screaming, then a frot is swimming. 
If a frot is swimming, then a greep is flinging.

• A blub is flinging.
• If a blub is screaming, then a greep is flinging.
• A frot is swimming when a blub is screaming.
• If a greep is flinging, then a blub is screaming.

Tags

CCSS.RI.11-12.2

CCSS.RI.9-10.1

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

Make a valid conclusion:
If it rains then the sky is dark.
If the sky is dark, then crickets will chirp.
Laura is using her umbrella.

• The crickets are chirping.
• They sky is dark.
• Laura is avoiding the rain.
• No conclusion can be made.

Tags

CCSS.RI.11-12.2

CCSS.RI.9-10.1

CCSS.RL.11-12.1

CCSS.RL.8.1

CCSS.RL.9-10.1

_________ circles has a radius of 18cm.

• All

• Some

 $"20\%\ of\ 30\ is\ 6\ if\ and\ only\ if\ 0.2\times30=6."$  Construct two appropriate implications based on the implication.

•  $p:\ 20\%\ of\ 30\ is\ 6$   $q:\ 0.2\times30=6$  

•  $p:\ 0.2\times\times30=6$   $q:\ 20\%\ of\ 30\ is\ 6$  

•  $\left(a\right)\ If\ 20\%\ of\ 30\ is\ 6,\ then\ 0.2\times30=6$   $\left(b\right)\ If\ 0.2\times30=6,\ then\ 20\%\ of\ 30\ is\ 6$  

•  $\left(a\right)\ If\ 0.2\times30=6,\ then\ 20\%\ of\ 30\ is\ 6$   $\left(b\right)\ If\ 20\%\ of\ 30\ is\ 6,\ then\ 0.2\times30=6$  

Determine whether this sentence is a statement or not. If yes, determine its truth value.

"Perak is located in Malaysia."

• Not a statement.

• Statement. False.

• Statement. True.