Answer:
See proof below
Step-by-step explanation:
An equivalence relation R satisfies
- Reflexivity: for all x on the underlying set in which R is defined, (x,x)∈R, or xRx.
- Symmetry: For all x,y, if xRy then yRx.
- Transitivity: For all x,y,z, If xRy and yRz then xRz.
Let's check these properties: Let x,y,z be bit strings of length three or more
The first 3 bits of x are, of course, the same 3 bits of x, hence xRx.
If xRy, then then the 1st, 2nd and 3rd bits of x are the 1st, 2nd and 3rd bits of y respectively. Then y agrees with x on its first third bits (by symmetry of equality), hence yRx.
If xRy and yRz, x agrees with y on its first 3 bits and y agrees with z in its first 3 bits. Therefore x agrees with z in its first 3 bits (by transitivity of equality), hence xRz.
Answer:
u=30
x=150
z=150
y=30
Step-by-step explanation:
u=y [ being vertically opposite angle]
x+u=180[ being linear pair]
x+30=180
x=180-30
x=150
z=x[being vertically opposite angle]
z=150
y=u[ being voa]
Answer: "Subtract 6 from both sides, and then divide by 2. The solution is x = 8"
Step-by-step explanation: Lets solve for 2x + 6 = 22
Step 1 Subtract 6 from both sides: 2x + 6 - 6 = 22 - 6 2x = 16
Step 2 Divide by 2 in both sides: 2x/2 = 16/2
Step 3 The answer: x = 8
Answer: 27 and 18
Step-by-step explanation:
x - y = 9 → x = 9 + y
3y = 2x
3y = 2(9 + y)
3y = 18 + 2y
3y - 2y = 18
y = 18
2x = 3(18)
2x = 54
x = 27
x - y = 9
27 - 18 = 9
9 = 9
