Tag: business maths

Quizzes (44) Questions (670)

Questions Related to business maths

Multiple choice logical equivalence mathematical logic discrete mathematics business maths maths

The only statement among the followings that is a tautology is

  1. $A\vee(A\wedge B)$
  2. $[A\wedge (A\rightarrow B)]\rightarrow B$
  3. $B\rightarrow [A\wedge (A\rightarrow B)]$
  4. $A\wedge (A\vee B)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Option B represents modus ponens, which is a universally valid argument form and thus a tautology. By constructing a truth table, we find that the conditional statement always evaluates to true.

Multiple choice logical equivalence mathematical logic discrete mathematics business maths maths

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

  1. $Tautology$
  2. $Contradiction$
  3. $P\wedge q$
  4. $p\wede(\sim q)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The expression (p -> q) ^ (q -> r) -> (p -> r) is a classic logical law known as the Hypothetical Syllogism. A truth table shows that it evaluates to True for all possible truth values of p, q, and r, making it a tautology.

Multiple choice logical equivalence mathematical logic discrete mathematics business maths maths

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

  1. a tautology

  2. a contradiction

  3. neither a tautology nor a contradiction

  4. both a tautology and a contradiction
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Analyzing the expression reveals an internal contradiction because it forces both p and not p to be true simultaneously. Therefore, the entire conjunction is always false, making it a contradiction.

Multiple choice logical equivalence mathematical logic discrete mathematics business maths maths

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

  1. $A\wedge (A\vee B)$
  2. $A\vee (A\wedge B)$
  3. $[A\wedge (A\rightarrow B)]\rightarrow B$
  4. $B\rightarrow [A\wedge (A\rightarrow B)]$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Option C represents the standard logical rule of detachment, or modus ponens, which is a tautology. Evaluating its truth table yields true in every row.

Multiple choice logical equivalence mathematical logic discrete mathematics business maths maths

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

  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 $2 ^ { 3 } = 5$
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

Multiple choice logical equivalence mathematical logic discrete mathematics business maths maths

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

  1. is a tautology
  2. is equivalent to $( p \wedge q ) \vee ( - q )$
  3. is equivalent to $p \vee q$

  4. is a contradiction
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The expression ~(p ^ q) v q is equivalent to (~p v ~q) v q. By associativity, this is ~p v (~q v q), which is ~p v T, which is T. Thus, it is a tautology.