Let p: the shape is a rhombus. let q: the diagonals are perpendicular. let r: the sides are congruent. which represents "the shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent”? p ∧ (q ∧ r) (p ∨ q) ∨ r p ↔ (q ∧ r) (p ∨ q) ↔ r

The correct answer would be, C p ↔ (q ∧ r).

 The correct option is (C) p ↔ (q ∧ r).

Step-by-step explanation:  We are given the following three statements :

p: The shape is a rhombus.

q: The diagonals are perpendicular.

r: The sides are congruent.

We are to select the correct statement that describes the following :

"The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent”.

We know that

if two statements are connected by 'AND', then we use the symbol ∧.

So, the statement "the diagonals are perpendicular and the sides are congruent” is written as

q ∧ r.

Also, it two statements are connected by 'if and only if', then we use the symbol ↔.

Therefore, the statement  "The shape is a rhombus if and only if the diagonals are perpendicular and the sides are congruent” is written as

p ↔ (q ∧ r).

Thus, (C) is the correct option.

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )