2. Give recursive definitions for the following sets. a. The set of all strings over {a, b} containing at least one "a". b. The set of odd-length binary strings that end with 00.

Answer and  explanation:

Recursive is related to repeat the definition, rule, and procedure.

a)The set of all strings over {a,b} containing at least one a.

Let x is a string containing at least one a: x=a and y= b

Sets of union of XY and yx will be (XY) (yx) = (a,b) (b, a)

b)The set of odd length binary strings that end with 00

There is a regular expression compared with two 00, which is surrounded by 0+1 with at least two 0s.

Fill up the .3 container and then pour it into the .5

fill up the .3 again and fill up the .5 ... if all is poured in the .5 will overflow over the top.

stop when the .5 is totally full... only .3 will fit... the liquid left in  the .3 will be .1

Step-by-step explanation: