Why is the empty set always a subset of every set?

here is something that relies on definition of subset and logical implication:

the definition of a subset is that if there are two sets a and b of a certain universe, a is a subset of b if every element in a is also an element of b, i.e.

  for all x, if x ∈ a, then x ∈ b

the empty set ∅ has no elements, so if a is any set from any universe, then ∅ ⊆ a (∅ is a subset of a) is true if

  for all x, if x ∈ ∅, then x ∈ a

clearly, x ∈ ∅ is always false because the empty set has no elements. so this implication is always true (remember that logical implication is only false if a true premise implies a false conclusion), thus making ∅ ⊆ a always true.

15

step-by-step explanation:

we are given the following expression and we are to solve it and find the product:

-13 × (-5)

solving the given expression in the standard order of solving a mathematical expression, beginning with the opening of brackets and then multiplying the terms and changing their signs.

-3 × -5 = 15 (answer is positive because when negative is multiplied with negative, it gives a positive answer)