Mathematical Logic

If  $p\wedge\ q\$  is false and  $p\vee q$  is true , then which of the following is not True.

•  $p\vee q$  

•  $p\leftrightarrow q$  

•  $\sim p\vee\sim q$  

•  $q\vee\sim p$  

Tags

CCSS.HSS.CP.A.1

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

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

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

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

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

Ifis F ,  $p\rightarrow q\$   is F then the truth values of p and q are

• T,T

• T,F

• F,T

• F,F

The negation of inverse of $\sim p\rightarrow q\$  is 

•  $q\wedge p$  

•  $\sim p\wedge\sim q$  

•  $p\wedge q$  

•  $\sim q\rightarrow\sim p$  

Tags

CCSS.HSS.CP.A.1

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

If A= {1,2,3,4,5} then which of the following is not True?

• $\exists\ x\in A$ such that x+3 = 8

• $\exists\ x\in A\$ such that x+2 <9

• $\forall\ x\in A$ , x+6 $\ge$ 9

• $\exists\ x\in A\$ such that x+6<10

Tags

CCSS.HSA.REI.B.3

CCSS.HSA.CED.A.1

CCSS.HSA.CED.A.3

CCSS.HSA.REI.B.4

CCSS.HSA.SSE.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.HSS.CP.A.1

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

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.