- #1

negation

- 818

- 0

## Homework Statement

S = { (x1, x2, x3, x4) | 4 x1 + x3 = 3 + 6 x2 + x4 }

T = { (x1, x2, x3, x4) | x1 + x3 is an integer }

U = { (x1, x2, x3, x4) | x1 x3 ≥ -5 }

## The Attempt at a Solution

a) Which of these subsets contain the zero vector 0 = (0, 0, 0, 0) ?

S = (x1,x2,x3,x4) = (0,0,0,0)

4x1 =x3 = 3+6x2 + x4

4(0) + 0 = 3+ 6(0) + 0

0=3

S is false

T = (x1,x2,x3,x4) = (0,0,0,0)

x1+x3 = integer and I assume that by 'integer' it implies relative integer such that 0 is an integer.

If we assume so, then,

x1 + x3 = 0 + 0 = 0

T is true

U = (x1,x2,x3,x4) = (0,0,0,0)

x1.x3 =>-5

0.0 = 0 but 0~= -5 but 0>-5

U is true.

b) Which of these subsets are subspaces of R4 ?