Form the compound statement by using basic connective "And" and "OR" from following statements.

$p:$ Rational number follows commutative property for addition.

$q:$ Rational number follows commutative property for multiplication.

 

Form the compound statement by using basic connective "And" and "OR" from following statement

$p:$ All sides of two congruent triangles are equal.

$q:$ All angles of two congruent triangles are same.

Check whether the given compound statement $p$ is true or false.

$p:$Chord of a circle lies within the circle and tangent of a circle lies both outside and inside of circle.

Check whether the given compound statement $p$ is true or false.

$p:$From a point outside the circle we can draw two tangent to a circle or from a point inside the circle we can draw one tangent to circle.

Identify the quantifier in the following statements and also write their negation.

$p:$ For every natural number $x,7 x$ is greater than $7$.

Identify the quantifier in the following statement and also write their negation.

$q:$ There exists a tangent which is chord to the circle.

Write the following statements in the form "if then"

$p:$ Three common tangent can be drawn to two circles if they touch each other.

Write the following statements in the form "if then"

$q:$ Chord of a circle which subtends an angle $90°$ in alternate segment implies it is diameter.

Given below are a two pair of statements combine these two statements using "if and only if'.

$p :$ If a convex polygon is pentagon then it has $5$ diagonals.

$q:$ If a convex polygon has $5$ diagonals then it is pentagon.