The tables below show the values of predicates p(x, y), q(x, y), and s(x, y) for every possible combination of values of the variables x and y. the row number indicates the value for x and the column number indicates the value for y. the domain for x and y is {1, 2, 3}.

p 1 2 3
1 t f t
2 t f t
3 t t f
q 1 2 3
1 f f f
2 t t t
3 t f f
s 1 2 3
1 f f f
2 f f f
3 f f f
indicate whether each of the quantified statements is true or false.

(a)

∃x ∀y p(x, y)

(b)

∃x ∀y q(x, y)

(c)

∃x ∀y p(y, x)

(d)

∃x ∃y s(x, y)

(e)

∀x ∃y q(x, y)

(f)

∀x ∃y p(x, y)

(g)

∀x ∀y p(x, y)

(h)

∃x ∃y q(x, y)

(i)

∀x ∀y ¬s(x, y)

answer: when the substance contain the two parts (polar and non-polar) like soap.

explanation:

soap is produced from the basic hydrolysis of ester "saponification", it is considered as a salt of hydrocarbons. the soap molecule contains the two parts: a polar group   (-coo-na+) and a non-polar group (r-hydrocarbon part). the polar group is called the head and the tail is the non-polar group. the polar group is hydrophilic in nature (water loving) and the non-polar group is hydrophobic in nature (water repelling).the polar/non-polar nature of a substance is useful that it can dissolve the non-polar substances by the polar part and also can dissolve the polar substances by the non-polar part. it commonly used in detergents and soaps.

Answerthe systems development lifecycle;