Let p(x, y) be a propositional function if ꓯyꓱxp(x, y) is true does it necessarily follow that ꓱxꓯyp(x, y) is true? justify your answer or give a counter-example

Ok, we know that ꓯ y ꓱ x P(x,y) is true, and suppose we are working with integers.

Lets create a counter-example

if P(x,y) : x = y, then for all integer y you can find another integer x such the proposition is true, and ꓯ y ꓱ x P(x,y) is true.

now the second part; ꓱ x ꓯyP(x,y) is true? this means that exist an x, such that p(x,y) is true for all the y in the domain. Now, is also easy to se that, for each x, there is only one y that keeps the proposition true, and is y = x.

So ꓱx ꓯy P(x,y) is not true

x² + 3x + 7 = 0       [ax² + bx + c]

a = 1

b = 3

c = 7

quadratic formula:

    (+/- is this ±)

plug in the numbers into the variables

your answer is a

i saw this question before, dont know the asnwer srry

step-by-step explanation: