Mathematical Logic

 $\left(p\wedge q\right)\rightarrow r\$  is logically equivalent to 

•  $p\rightarrow\left(q\rightarrow r\right)$  

•  $\left(p\wedge q\right)\rightarrow\sim r$  

•  $\left(\sim p\vee\sim q\right)\rightarrow\sim r$  

•  $\left(p\vee q\right)\rightarrow r$  

The negation of $p\wedge\left(q\rightarrow r\right)$ is 

•  $\sim p\wedge\left(\sim q\rightarrow\sim r\right)$  

•  $p\vee\left(\sim q\vee r\right)$  

•  $\sim p\wedge\left(\sim q\rightarrow\sim r\right)$  

•  $\sim p\vee\left(\sim q\wedge\sim r\right)$  

Tags

CCSS.HSS.CP.A.1

Examine  $\left(p\wedge q\right)\wedge\left(\sim p\vee\sim q\right)$  

• Tautology

• Contradiction

• Contingency

• None of these

Tags

CCSS.HSS.CP.A.1

Dual of  $\left(p\wedge t\right)\vee\left(c\wedge\sim q\right)$  

•  $\left(p\vee c\right)\wedge\left(t\wedge q\right)$  

•  $\left(p\vee c\right)\wedge\left(c\wedge\sim q\right)$  

•  $\left(p\wedge c\right)\vee\left(t\wedge q\right)$  

•  $\left(p\vee c\right)\wedge\left(t\vee\sim q\right)$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSS.CP.A.1

7>3 and 4 >11 Negation of Statement is

• $7<3\ or\ 4<11$

• $7\le3\ and\ 4\le11$

• $7\le3\ or\ 4\le11$

• $7\ne3\ and\ 4\ne11$

Tags

CCSS.HSA.REI.B.3

"If a Function is differentiable then it is Continuous."What is Contra-positive of Statement .

• If a function is not continuous then it is not differentiable

• If a function is not differentiable then it is not continuous.

• If a function is continuous then it is differentiable

• If a function is not continuous then it is differentiable.

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. 

If $p$ and  $q$ are two statements, then statement  $p\longrightarrow q\ \wedge\sim q$  is

• Tautology

• Contradiction

• Neither Tautology nor contradiction

• None of the above

Let $p\wedge\left(q\vee r\right)=\left(p\wedge q\right)\vee\left(p\wedge r\right)$ .
Then, this law is known as.......

• Commutative Law
  

• Associative law

• De-Morgan's Law

• Distributive Law

Truth value of the statement "if p then q" is false when

• p is true, q is true

• p is true, q is false

• p is false, q is true

• p is false, q is false