Question

5. Which of the following are the example of null seil?​

Answer 1

Answer:

Perhaps what you find confusing is the use of set-builder notation to define P,Q,R: Included in between { ... } are the condition(s) that any "candidate" element must satisfy in order to be included in the set, and a set defined by set-builder notation contains all, and only, those elements satisfying all the conditions given.

In each of P,Q,R, set-builder notation is used to provide the conditions for inclusion in each set, respectively. Note: unless otherwise stipulated, you can take conditions separated by a comma to be a conjunction of conditions; that is:

X={x:(condition 1), (condition 2), ...., (condition n)}

means X is the set of all x such that x satisfies (condition 1) AND x satisfies (condition 2) AND ... AND x satisfies (condition n).

P={x:x2=4,x is odd}

The only solution to x2=4 are x=−2 or x=2, neither of which is odd. Hence there are no elements in P; that is, P=∅.

Q={x:x2=9,x is even}

The only solutions to x2=9 are x=−3 or x=3, neither of which is even. Hence, there are no elements in Q; that is, Q=∅.

R={x:x2=9,2x=4}

x=2 is the only solution to 2x=4, but x=2 is not a solution to x2=9, (and neither x=3 nor x=−3 is a solution to 2x=4). Hence, there are no elements in R; that is, R=∅.

NOTE: As an aside, regarding notation - sometimes instead of a colon :preceding the defining characteristics of a given element, you'll see | in place of the colon. E.g.,

P={x:x2=4,x is odd}⟺{x∣x2=4,x is odd}