2-2A #2 Rewrite the following using mathematical symbols:
a. P is equal to the set containing a, b, c, and d.
b. The set consisting of the elements 1 and 2 is a proper
subset of {1, 2, 3, 4}
c. The set consisting of the elements 0 and 1 is not a
subset of {1, 2, 3, 4}
d. 0 is not an element of the empty set.
a. P = {a, b, c, d}
To write it using mathematical symbols, we use the curly brackets to represent a set and commas to separate the elements within the set. So, P is equal to the set {a, b, c, d}.
b. {1, 2} ⊆ {1, 2, 3, 4}
To represent that the set consisting of the elements 1 and 2 is a proper subset of {1, 2, 3, 4}, we use the subset symbol (⊆). It means that all the elements of the set on the left are also elements of the set on the right, and there can be additional elements in the set on the right. In this case, the set {1, 2} is a proper subset of {1, 2, 3, 4}.
c. {0, 1} ⊈ {1, 2, 3, 4}
To represent that the set consisting of the elements 0 and 1 is not a subset of {1, 2, 3, 4}, we use the subset with a stroke symbol (⊈). It means that the set on the left is not a subset of the set on the right, as it contains at least one element that is not present in the set on the right. In this case, the set {0, 1} is not a subset of {1, 2, 3, 4}.
d. 0 ∉ ∅
To represent that 0 is not an element of the empty set, we use the not an element symbol (∉). It means that the element on the left is not present in the set on the right. In this case, 0 is not an element of the empty set (∅).