Mathematical Logic

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

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

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

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

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

 $p\vee\left(\sim q\vee r\right)$  

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

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

Tautology

Contradiction

Contingency

None of these

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

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

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

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

$7<3\ or\ 4<11$

$7\le3\ and\ 4\le11$

$7\le3\ or\ 4\le11$

$7\ne3\ and\ 4\ne11$

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.

Tautology

Contradiction

Neither Tautology nor contradiction

None of the above

Commutative Law

Associative law

De-Morgan's Law

Distributive Law

p is true, q is true

p is true, q is false

p is false, q is true

p is false, q is false