Q.Which of the following statements are true and which are false? In each case give a valid reason for saying so.

1. p: "Each radius of a circle is a chord of the circle." A chord is a line segment with both endpoints on the circle. A radius has one endpoint at the centre (not on the circle) and one on the circle. False.
2. q: "The centre of a circle bisects each chord of the circle." This is only true for chords passing through the centre (diameters); a chord not through the centre is not bisected by it. False.
3. r: "Circle is a particular case of an ellipse." An ellipse with semi-major axis equal to semi-minor axis (eccentricity 0) is exactly a circle. True.
4. s: "If x and y are integers such that x > y, then $-x < -y$." Multiplying both sides of an inequality by a negative number ($-1$) reverses the direction of the inequality: $x > y \Rightarrow -x < -y$. True. …

For each claim, recall the exact definition (chord needs both endpoints on the circle; bisection by centre only for diameters; ellipse generalizes circle; inequality reversal under multiplication …

• Confusing a radius with a chord — a radius touches the circle at only one point.
• Forgetting the inequality-reversal rule when multiplying by a negative number. …