Converse

Q. If $P$ and $Q$ are two statements, then which of the following compound statements is a tautology?

1. $((P\Rightarrow Q)\wedge \sim Q)\Rightarrow P$
2. $((P\Rightarrow Q)\wedge \sim Q)\Rightarrow \sim P$
3. $((P\Rightarrow Q)\wedge \sim Q)\Rightarrow (P\wedge Q)$
4. $((P\Rightarrow Q)\wedge \sim Q)\Rightarrow Q$

Q. The converse of the contrapositive of the conditional statement $\sim p\to q$ is

1. $p\to \sim q$
2. $q\to p$
3. $p\to q$
4. $\sim q\to p$

Q. Converse of the statement " If $n^{th}$ term of a sequence is linear then sequence is in A.P."is

1. If a sequence is not in A.P. then its $n^{th}$ term is linear
2. If a sequence is in A.P. then its $n^{th}$ term is not linear
3. If a sequence is in A.P. then its $n^{th}$ term is linear
4. If a sequence is not in A.P. then its $n^{th}$ term is not linear.

Q. If $P$ and $Q$ are two statements, then which of the following compound statements is a tautology?

1. $((P\Rightarrow Q)\wedge \sim Q)\Rightarrow P$
2. $((P\Rightarrow Q)\wedge \sim Q)\Rightarrow \sim P$
3. $((P\Rightarrow Q)\wedge \sim Q)\Rightarrow (P\wedge Q)$
4. $((P\Rightarrow Q)\wedge \sim Q)\Rightarrow Q$

Q. The converse of the contrapositive of the conditional $p\to \sim q$ is.

1. $p\to q$
2. $\sim q\to p$
3. $\sim p\to q$
4. $\sim p\to \sim q$

Q. The converse of the contrapositive of the conditional $p\to \sim q$ is :

1. $p\to q$
2. $\sim p\to \sim q$
3. $\sim p\to q$
4. $\sim q\to p$

Q. Write converse of statement. In $\Delta ABC$, if $AB=AC$ then $\angle C=\angle B$.

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

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

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

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

Q. The converse of $p\Rightarrow q$, is

1. $q\Rightarrow p$
2. $\sim p\Rightarrow \sim q$
3. $\sim q\Rightarrow \sim p$
4. $p\Rightarrow q$

Q. Write the converse and contrapositive of the following statement:
If $x+3=9$, then $x=6$.

Q. Write the converse and contrapositive of each of the following:
If a positive integer $n$ is divisible by $9$, then the sum of its digits is divisible by $9$

Q. Statement the converse and contrapositive of each of the following statements:
A positive integer is prime only if it has no divisors other than $1$ and itself.

Q. Write the converse of the following statement. If the sum of measures of angles in a figure is ${180}^{\circ }$, then the figure is a triangle.

Q. The converse of the statement "if $p<q$, then $p-x<q-x$" is :

1. If $p-x>q-x$, then $p>q$
2. If $p>q$, then $p-x>q-x$
3. If $p<q$, then $p-x>q-x$
4. If $p-x<q-x$, then $p<q$

Q. 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

Q. Converse of the statement " If $n^{th}$ term of a sequence is linear then sequence is in A.P."is

1. If a sequence is not in A.P. then its $n^{th}$ term is linear
2. If a sequence is in A.P. then its $n^{th}$ term is not linear
3. If a sequence is in A.P. then its $n^{th}$ term is linear
4. If a sequence is not in A.P. then its $n^{th}$ term is not linear.

Q. Write the converse, inverse and contrapositive of the following statement :
A family becomes literate if the women in it are literate.

Q. Write converse , inverse and contrapositive of the following statements.
If voltage increases then current decreases.

Q. Write the converse of the following statement. If the corresponding angles formed by a transversal of two lines are congruent then the two lines are parallel.

Q. Write the converse and contrapositive of each of the following:
If the two lines are parallel, then they do not intersect in the same plane.

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

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.