Tag: business maths

Questions Related to business maths

The only statement among the followings that is a tautology is

logical equivalence mathematical logic discrete mathematics business maths maths

  1. $A\vee(A\wedge B)$

  2. $[A\wedge (A\rightarrow B)]\rightarrow B$

  3. $B\rightarrow [A\wedge (A\rightarrow B)]$

  4. $A\wedge (A\vee B)$

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Correct Option: A

The simplifed form of $(p \vee q)\vee (\sim p \wedge q)$ is

logical equivalence mathematical logic discrete mathematics business maths maths

  1. $T$

  2. $p \wedge q$

  3. $F$

  4. $p \vee q$

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Correct Option: A

$p,q,r$ are $3$ statements such that $\left(p\rightarrow q\right)\wedge \left(q\rightarrow r\right)=Rightarrow \left(p\rightarrow r\right)$ is

logical equivalence mathematical logic discrete mathematics business maths maths

  1. $Tautology$

  2. $Contradiction$

  3. $P\wedge q$

  4. $p\wede(\sim q)$

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Correct Option: A

If p, q two propositions then $(p \vee \sim q) \wedge ( \sim p \wedge q)$ is

logical equivalence mathematical logic discrete mathematics business maths maths

  1. a tautology

  2. a contradiction

  3. neither a tautology nor a contradiction

  4. both a tautology and a contradiction

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Correct Option: A

The only statement among the following taht is a tautology is -

logical equivalence mathematical logic discrete mathematics business maths maths

  1. $A\wedge (A\vee B)$

  2. $A\vee (A\wedge B)$

  3. $[A\wedge (A\rightarrow B)]\rightarrow B$

  4. $B\rightarrow [A\wedge (A\rightarrow B)]$

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Correct Option: A

The contrapositive of the statement "if  $2 ^ { 2 } = 5 ,$  then  $1$  get first class" is

logical equivalence mathematical logic discrete mathematics business maths maths

  1. If I do not get a first class, then $2 ^ { 2 } = 5$

  2. If I do not get a first class, then $2 ^ { 2 } \neq 5$

  3. If I get a first class, then $2 ^ { 2 } = 5$

  4. If I get a first class, then $2 ^ { 3 } = 5$

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Correct Option: B
Explanation:

$P:{ 2 }^{ 2 }=5$

$q:I$ get first class
the contrapositive of $p\rightarrow q$ is $\sim q\rightarrow \sim p$. Hence the answer is if $I$ do not get a first class, then ${ 2 }^{ 2 }\neq 5$
Correct Answer : Option B.

The proposition $( P \Longrightarrow \sim p) ^ (\sim p \Longrightarrow P)$ is 

logical equivalence mathematical logic discrete mathematics business maths maths

  1. Contingency

  2. Neither Tautology nor contradiction

  3. contradiction

  4. Tautology

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Correct Option: A

Which of  the following is logically equivalent to : $\sim \left[\sim p\rightarrow q\right]$

logical equivalence mathematical logic discrete mathematics business maths maths

  1. $p\vee\sim q$

  2. $\sim p\wedge q$

  3. $\sim p\vee q$

  4. $\sim p\wedge \sim q$

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Correct Option: A

The statement  $\sim ( p \wedge q ) \vee q$

logical equivalence mathematical logic discrete mathematics business maths maths

  1. is a tautology

  2. is equivalent to $( p \wedge q ) \vee ( - q )$

  3. is equivalent to $p \vee q$

  4. is a contradiction

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Correct Option: A

The simplicity $ \sim(p \rightarrow q) \longleftrightarrow(\sim p \vee \sim q) $ is

logical equivalence mathematical logic discrete mathematics business maths maths

  1. tautology

  2. contradiction

  3. neither t nor e

  4. None of these.

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Correct Option: A