Tag: euclid's postulates

Questions Related to euclid's postulates

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

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

  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

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Correct Option: A
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."

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

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

  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

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Correct Option: B
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 $B$.

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

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

  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.

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Correct Option: A
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.

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

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

  1. $(q \wedge \sim r) \vee p$

  2. $(\sim q \vee r) \vee p$

  3. $(q \wedge \sim r) \wedge \sim p$

  4. $(q \wedge \sim r) \wedge p$

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Correct Option: A
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 $

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

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

  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

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Correct Option: B
Explanation:

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

According to Euclid, a surface has ____.

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

  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

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Correct Option: B
Explanation:

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

Euclid stated that all right angles are equal to each other in the form of

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

  1. an axiom

  2. a definition

  3. a postulate

  4. a proof

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Correct Option: C
Explanation:

Euclid's fourth Postulate states that all right angles are equal to each other.

Ans- Option C.

Use Euclid's division algorithm to find the HCF of 
$867$ and $255$

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

  1. $50$

  2. $51$

  3. $41$

  4. $3$

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Correct Option: B

___________ was the most logical and abstract creator of Euclid's geometry approach.

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

  1. Hilbert

  2. Bhasharacharya

  3. Thelus

  4. Pythagorous

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Correct Option: D
Explanation:

Pythagoras developed the theory of geometry to a great extent.

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.

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

  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

Show answer
Correct Option: B
Explanation:

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