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:
Step-by-step explanation:
Answer:
(n-14) / n
Step-by-step explanation:
n is your number;
"14 less" means "subtract 14", --> we have (n-14);
now we need to divide (n-14) by same number as your number, which is "n"---> final expression is: (n-14)/n
All it takes for a relation to be a function is for each possible first number of a pair there's only one possible second number.
So if any of the sets has two pairs with the same first number, that one's not a function.
The last one has (3,2) and (3,5) so isn't a function.
Q57) if 1/4 of a packet cover 1/5 then using a packet is using 4* 1/4 of it. This means that 4*1/5 of the garden would be covered which = 4/5.
q58) the total is 24 and 9 of them are boys. Therefore it follows that 9/24 of them are boys and so thats the probability of choosing a boy at random.
