Suppose that the domain of the propositional function p(x) consists of −5, −3, −1, 1, 3, and 5. express these statements without using quantifiers, instead using only negations, disjunctions, and conjunctions.

a) ∃xp (x)
b) ∀xp (x)
c) ∀x((x ≠ 1) → p (x))
d) ∃x((x ≥ 0) ∧ p (x))
e) ∃x(¬p (x)) ∧ ∀x((x < 0) → p (x))

check the picture below.

19.

step-by-step explanation:

you add the 9 in the tens column since it is a single digit and 9 plus zero is 9 so it is 19

4

step-by-step explanation:

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

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