Tag: implications

Quizzes (0) Questions (105)

Questions Related to implications

Multiple choice business maths mathematical reasoning implications principle of mathematical induction proofs in mathematics

Given, "If I have a Siberian Husky, then I have a dog." Identify the converse

  1. If I do not have a Siberian Husky, then I do not have a dog.

  2. If I have a dog, then I have a Siberian Husky.

  3. If I do not have a dog, then I do not have a Siberian Husky.

  4. If I do not have a Siberian Husky, then I have a dog.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The converse of 'If P then Q' is 'If Q then P'. Thus, the converse of 'If I have a Siberian Husky, then I have a dog' is 'If I have a dog, then I have a Siberian Husky'.

Multiple choice business maths mathematical reasoning implications principle of mathematical induction proofs in mathematics

$∼(p⇒q)⟺∼p\vee ∼q  \, is$

  1. a tautology

  2. a contradiction

  3. neither a tautology nor a contradiction

  4. cannot come to any conclusion
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The expression ~(p -> q) is equivalent to (p AND ~q). The expression (~p OR ~q) is the negation of (p AND q). These are not equivalent, so the statement is neither a tautology nor a contradiction.

Multiple choice business maths proofs in mathematics implications principle of mathematical induction different forms of theoretical statements

Consider the following statements 
$p$:you want to success
$q$:you will find way,
then the negation of $\sim (p\vee q)$ is

  1. you want of success and you find a way

  2. you want of success and you do not find a way

  3. if you do not want to succeed then you will find a way

  4. if you want of success then you cannot find a way
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice business maths proofs in mathematics implications principle of mathematical induction different forms of theoretical statements

Which of the following statements is a tautology

  1. $\left( { \sim p \vee q} \right) - \left( {p \vee \sim q} \right)$
  2. $\left( { \sim p \vee \sim q} \right) \to p \vee q$
  3. $\left( {p \vee \sim q} \right) \wedge \left( {p \vee q} \right)$
  4. $\left( { \sim p \vee \sim q} \right) \vee \left( {p \vee q} \right)$
Reveal answer Fill a bubble to check yourself
C Correct answer
Multiple choice business maths proofs in mathematics implications principle of mathematical induction different forms of theoretical statements

The statement $p \to (q \to p)$ is equivalent to 

  1. $p \to q$
  2. $p \to (q \vee p)$
  3. $p \to (q \to p)$
  4. $p \to (q \wedge p)$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The statement p -> (q -> p) is equivalent to p -> (~q OR p), which is ~p OR (~q OR p). This simplifies to (~p OR p) OR ~q, which is True OR ~q = True. Option B is also a tautology, but the equivalence is not standard.

Multiple choice business maths proofs in mathematics implications principle of mathematical induction different forms of theoretical statements

Which of the following is correct?

  1. $(~p \vee ~q) \equiv (p \wedge q)$
  2. $(p \rightarrow q) \equiv (~q \rightarrow ~p)$
  3. $~(p \rightarrow ~q) \equiv (p \wedge ~q)$
  4. $~(p \leftrightarrow q) \equiv (p \rightarrow q) \wedge (q \rightarrow p)$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation


$~(p \leftrightarrow q) \equiv (p \rightarrow q) \wedge (q \rightarrow p)$ is true, we show it by truth table using boolean expression.

1.$p\rightarrow q$=min(1,1+q-p)
2.$p\wedge q$=min(p,q)
3.$p\leftrightarrow q$=1-|p-q|

Now we draw or make truth table using these operations
L.H.S  

 p  q $p\leftrightarrow q$ 
 1 1  1 
1  0  0 


R.H.S 

p q  $p\rightarrow q$  $q\rightarrow p$   $(p \rightarrow q) \wedge (q \rightarrow p)$
1  1  1  1  1
1  1  0 1  0 

L.H.S =R.H.S

$~(p \leftrightarrow q) \equiv (p \rightarrow q) \wedge (q \rightarrow p)$