if you can\'t read it , Let the statement P(x)= a real number x is equal to zero

Question

if you can't read it , Let the statement P(x)= a real number x is equal to zero,and use symbolic logic to represent the following statement. "If xy=0 then either x=0 or y=0" Also negate the statement in symbolic logic
So my teacher said to use quantification but I don't know where I would use that?

Let the statement P (x)= a real number x is equal to zero, and use symbolic logic ( P implies Q ) to represent the following statements. "If xy=0 , then either x=0 or y=o". Once that is done, negate the statement in symbolic logic and also write the negation out in english.

Explanation / Answer

Let,

P: a real number x is equal to zero, ie., x R, x =0

Q: a real number y is equal to zero, i.e., y R, y=0

R : product of two real nos. x*y is equal to zero, i.e., x, y R, xy =0

Now, the statement “If xy =0, then either x = 0 or y = 0” can be written symbolically as,

R (P v R)

The negation of the above statement can be written as,

~[ R (P v R)] = P ~ Q

Which can be written in English as;

For xy =0, x = 0 and y 0

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.