Tag: euclid's postulates

Questions Related to euclid's postulates

Complete the sentence with the most suitable option:
A: Robert is unhappy because he can't find his passport.
B: If only he __________________.

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

  1. Could have found it

  2. Had been able to find

  3. Could find it

  4. Had found it

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Correct Option: C

Complete the sentence with the most suitable option:
A: Mary is sorry that she bought such an expensive dress.
B: If only she ________________ such an expensive dress.

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

  1. Didn't but

  2. Wouldn't have bought

  3. Hadn't bought

  4. Could have bought

Show answer
Correct Option: C

Identify the conditional phrase in the following sentence from the options given below:
If the police had arrived a bit early, the thief would have easily been caught.

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

  1. Future Result

  2. Imaginative Counterfactual

  3. Factual Conditions

  4. Imaginative Hypothetical

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Correct Option: B
Explanation:

Since the situation posited is imaginative and expresses a speculative condition, Option B is correct. The rest of the options do not present an unlikely condition, hence incorrect. 

Identify the conditional phrase in the following sentence from the options given below:
If you give the details by today evening, the payment would be credited tomorrow.

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

  1. Imaginative Counterfactual

  2. Factual Timeless

  3. Future Result

  4. None of these

Show answer
Correct Option: C
Explanation:

Since the situation posited and its consequences are to happen in future, Option C is correct. The rest of the options do not present a futurist condition, hence incorrect. 

What is true about the statement "If two angles are right angles the angles have equal measure" and its converse "If two angles have equal measure then the two angles are right angles"?

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

  1. The statement is true but its converse is false

  2. The statement is false but its converse is true

  3. Both the statement and its converse are false

  4. Both the statement and its converse are true

Show answer
Correct Option: A
Explanation:

Two right angles are always equal, each measuring 90 degrees.

However,  two equal angles can be anything not necessarily equal to 90 degrees always.
Hence $A$ is correct.

The converse of "if $x\in A\cap B$ then $x\in A$ and $x\in B$", is

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

  1. If $x\in A$ and $x\in B$, then $x\in A\cap B$.

  2. If $x\not\in A\cap B$, then $x\not\in A$ or $x\not\in B$.

  3. If $x\not\in A$ or $x\not\in B$, then $x\not\in A\cap B$.

  4. If $x\not\in A$ or $x\not\in B$, then $x\in A\cap B$.

Show answer
Correct Option: A
Explanation:

The converse of "If P then Q" is "If Q then P"
Hence, Option A

The converse of "If in a triangle $ABC, AB=AC$, then $\angle B=\angle C$", is

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

  1. lf in a triangle $ABC, \angle B=\angle C$, then $AB=AC$.

  2. lf in a triangle$ABC, AB\neq AC$, then $\angle B\neq\angle C$.

  3. lf in a triangle $ABC, \angle B\neq\angle C$, then $AB\neq AC$.

  4. lf in a triangle $ABC, \angle B\neq\angle C$, then $AB=AC$ .

Show answer
Correct Option: A
Explanation:

Take $p:AB=AC$

and $q:\angle B=\angle C$
So the given statement is symbolically represented as $p\rightarrow q$
Now by definition, Converse of a conditional statement $p\rightarrow q$ is $q\rightarrow p$
So $q\rightarrow p$ is given by 
"If in a triangle $ABC, \angle B=\angle C,$ then $AB=AC.$"

Which of the following is the converse of the statement: "If x>4 then x+2>5"?

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

  1. If x+2<5 then x<4

  2. If x is not greater than 4 then x+2 is not greater than 5

  3. If x+2>5 then x>4

  4. If x+2 is not greater than 5 then x is not greater than 4

Show answer
Correct Option: C
Explanation:
Converse of  "If  $A$  then  $B$"   is   "If  $B$  then  $A$".    Hence,
Converse of  "If  $x>4$  then  $x+2>5$"  will be  "If  $x+2>5$   then  $x>4$"
So, $C$ is correct.

The converse of "If $x$ has courage, then $x$ will win", is

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

  1. If $x$ wins, then $x$ has courage.

  2. If $x$ has no courage, then $x$ will not win.

  3. If $x$ will not win, then $x$ has no courage.

  4. If $x$ will not win, then $x$ has courage.

Show answer
Correct Option: A
Explanation:

Take $p:x$ has courage

and $q:x$ will win
So the given conjugation is $p\Rightarrow q$

Now we need to find converse of this.
Be definition, Converse will be $q\Rightarrow p$
This is symbolic for "If $x$ wins then $x$ has courage

The converse of "if in a triangle $ABC, AB>AC$, then $\angle C=\angle B$", is

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

  1. lf in a triangle $ABC, \angle C=\angle B$, then $AB>AC$.

  2. lf in a triangle$ABC, AB\not\simeq AC$, then $\angle C\not\simeq \angle B$.

  3. lf in a triangle $ABC, \angle C\not\simeq \angle B$, then $ AB\not\simeq AC$.

  4. lf in a triangle $ABC, \angle C\not\simeq \angle B$, then $AB>AC$.

Show answer
Correct Option: A
Explanation:

Take $p:AB>AC$

and $q: \angle C=\angle B$
So the given statement is symbolically represented as $p\rightarrow q$
Now by definition, Converse of a conditional statement $p\rightarrow q$ is $q\rightarrow p$
Thus $q\rightarrow p$ is given by
"If in a $\triangle ABC, \angle C=\angle B$ then $AB>AC$."