Final answer:
Statement C, Z⊂R+, is false because the set of all integers (Z) includes negatives, which are not in the set of all positive real numbers (R+). The correct statement is Z-⊂R. Option C
Step-by-step explanation:
The question asks to identify the false statement among the given options which pertain to set notation and number sets. Here, the symbol '⋅' is used to denote that one set is a subset of another, meaning all elements of the first set are also in the second set. Let's evaluate each statement:
A. Z⊂R is true since Z (the set of all integers) is indeed a subset of R (the set of all real numbers).
B. Z+⊂N is true because Z+ (the set of all positive integers) is a subset of N (the set of natural numbers).
C. Z⊂R+ is false because Z (the set of all integers) includes negative numbers which are not in R+ (the set of all positive real numbers). The correct statement would be Z- (the set of all negative integers and zero) ⊂ R.
D. Z⊄R is true because the symbol '⊄' denotes 'is a subset of or equal to', and Z is indeed a subset of R.
Therefore, from the options given, the false statement is C. Z⊂R+. Option C