Negate the following statements and determine which is true, the statement or its negation. (a) P: 3K ER, Vn e N, 1/n > K. (b) Q: VxR, 3 € (0, ∞), Vy ≤ (x − ɛ, x + ε), y ‡ 1. (c) R: Vz € C, |z| < 1 ⇒ |z| < |z − i|.

the last three

2 In R show that 2 2 @ 2 ||× 11 ²2 + 2 |1y|1²³ = 11x +y|l² + 11 ×x -yll ² (Parollelogram Lou). _b.) 11 = ~y|| 11 x +yll ≤ 11 + 11² +11 11² 2 2 (.) 4(x,y) = 11x +y|l1² - 11 x-y11² (this is called the polarization identity

What geometric transformation of 3D space happens in this matrix-vector multiplication? 010 -1 0 0 0 01 9).( (3) Please note: All rotation directions to be understood as when looking along the rotation axis towards the origin. O Clockwise rotation by 90 degrees around the x3 axis Counter-clockwise rotation by 90 degrees around the x3 axis Clockwise rotation by 90 degrees around the x₂ axis Counter-clockwise rotation by 90 degrees around the x2 axis O Clockwise rotation by 90 degrees around the x₁ axis Counter-clockwise rotation by 90 degrees around the x₁ axis O Mirroring across the x₁-x2 plane Mirroring across the x₁-x3 plane Mirroring across the X₂-X3 plane