Question

Let P(x,y) be the statement “x+y=y”,where the domain consists of all real numbers. The truth value of
the quantification∃x∀y P(x,y) ,

is it true ? because when I saw a solved example it says true , but I don't think it's true ! what do you guys think ?

Answer 1

Also check this one:

Let C(X) be " x can program in C++ ", J(X) be "x can program in Java", where the domain consists
of all CCIS students.The statement"any student who can program in C++ can program in java" can be expressed as:

∀x (C(X) → J(X)) is it true ? or should I put and instead of then ?

Answer 2

∃x∀y P(x,y) means that there exists a value "x" such that for all "y", "x+y=y".

Answer 3

which is obviously true

Answer 4

"any student who can program in C++ can program in java" can be rephrased as:
"for all students X who can program in C++, X can program in java"

Answer 5

the second one should be then right ?

Answer 6

yes

Answer 7

thanks

Answer 8

no problem

Answer 9

back to the original question. It's true. Let x = 0, the 0 + y = y, for all y