Tag: conditional statements and converse

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Questions Related to conditional statements and converse

Multiple choice business maths basic concepts in geometry conditional statements and converse euclid's postulates introduction to euclid's geometry

Which of the following statements is the converse of "If the moon is full, then the vampires are prowling."?

  1. If the vampires are prowling, then the moon is full.

  2. If the moon is not full, then the vampires are prowling

  3. If the vampires are not prowling, then the moon is not full.

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Converse of  "If $P$, then $Q$"  is  "If $Q$, then $P$"

Similarly, option "$A$" is converse of the given statement  "If the moon is full, then the vampires are prowling."

Multiple choice business maths basic concepts in geometry conditional statements and converse euclid's postulates introduction to euclid's geometry

Which of the following statements is the converse of "You cannot skateboard if you do not have a sense of balance."?

  1. If you cannot skateboard, then you do not have a sense of balance.

  2. If you do not have a sense of balance, then you cannot skateboard.

  3. If you skateboard, then you have a sense of balance.

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Converse of "If $P$, then $Q$"  is  "If $Q$, then $P$". 

Now, the given statement  "You cannot skateboard if you do not have a sense of balance." can be re-written as "If you do not have a sense of balance, then you cannot skateboard."
The converse of this statement is option $B$.

Multiple choice business maths basic concepts in geometry conditional statements and converse euclid's postulates introduction to euclid's geometry

Which of the following statements is the contrapositive of the statement, You win the game if you know the rules but are not overconfident.

  1. If you lose the game then you dont know the rules or you are overconfident.

  2. A sufficient condition that you win the game is that you know the rules or you are not overconfident.

  3. If you dont know the rules or are overconfident you lose the game

  4. If you know the rules and are overconfident then you win the game.
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Contrapositive is the inverse of the converse of the statement.

It is obtained by first interchanging the hypothesis and conclusion and then adding "not" to both
In this case, converse is "If you win the game, then you know the rules but are not overconfident."
Inverse of this statement gives answer as A.

Multiple choice business maths basic concepts in geometry conditional statements and converse euclid's postulates introduction to euclid's geometry

The converse of $p \rightarrow (q \rightarrow r)$ is

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

The converse of $p \rightarrow (q \rightarrow r)$ is,

$\equiv (q \to r) \to p \equiv (\sim q \vee r) \to p \equiv  \sim (\sim q \vee r) \vee p\equiv (q \wedge \sim r) \vee p $

Multiple choice business maths basic concepts in geometry conditional statements and converse euclid's postulates introduction to euclid's geometry

Which of the following statements is the contrapositive of "If a polygon has four sides, then it is called a quadrilateral."?

  1. If a polygon is called a quadrilateral, then it has four sides.

  2. If a polygon is not called a quadrilateral, then it does not have four sides

  3. If a polygon does not have four sides, then it is not called a quadrilateral.

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Contrapositive will switch if and then and also add not to both parts.
Option B is correct.

Multiple choice maths introduction to euclid's geometry euclid's fifth postulate conditional statements and converse euclid's postulates

According to Euclid, a surface has ____.

  1. Length but no breadth and thickness

  2. Length and breadth but no thickness

  3. No length, no breadth and no thickness

  4. Length, breadth and thickness
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

According to Euclid a surface is a two-dimension plane without any volume, hence it has length and breath but no thickness.

Multiple choice maths introduction to euclid's geometry euclid's fifth postulate conditional statements and converse euclid's postulates

STATEMENT -1 : Given positive integers a and b, there exist whole numbers q and r satisfying a $=$ bq + r, 0 $\leq$ r  < b.
STATEMENT -2 : Any positive odd integer is of the form 6q+1, or 6q+3, or 6q+5, where q is some integer.

  1. Statement - 1 is True, Statement - 2 is True, Statement - 2 is a correct explanation for Statement - 1

  2. Statement - 1 is True, Statement - 2 is True ; Statement - 1 is NOT a correct explanation for Statement - 1

  3. Statement - 1 is True, Statement - 2 is False

  4. Statement - 1 is False, Statement - 2 is True
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Both the statements are true but statement - 2 is not a correct explanation for statement - 1.