Sales increased 50% last year, from $5,000 to $10,000. When sales dropped from $10,000 to $5,000 this year, sales decreased 50%
Answer:
hello your question is incomplete below is the missing parts
(a) A\ (A\B) = B\(B\A)
(b) A\ (BA) = B\(A\B)
answer : A\ (A\B) = B\(B\A) = always true
A\ (BA) = B\(A\B) = sometimes true and sometimes false
Step-by-step explanation:
(a) A\ (A\B) = B\(B\A). = ALWAYS TRUE
using de Morgan's law to prove this
A\ (A\B) = A\ ( A ∩ B^c )
= A ∩ ( A^C ∪ B )
= ( A ∩ A^C ) ∪ ( A ∩ B )
= Ф ∪ ( A ∩ B )
= ( A ∩ B )
ALSO : B\(B\A) = attached below is the remaining parts of the solution
B) A\ (BA) = B\(A\B) = Sometimes true and sometimes false
attached below is the prove using De Morgan's law
A 33 pound bag of grass seed has = 2 pounds less than 5 smaller bags of seed
= 33 pounds = 2 pounds less than 5 smaller bags
Let the weight of smaller bag of seed be ' x ' . Then ,
= 33 = 5x - 2
= 5x -2 = 33
= 5x = 33 + 2 ( transposing -2 from LHS to RHS changes -2 into +2 )
= 5x = 35
= x = 35 ÷ 5 ( transposing ×5 from LHS to RHS changes ×5 to ÷5 )
= x = 7 = weight of smaller bag of seed
Then , the weight of smaller bag of seed will be 7 pounds . Let us check it by putting 7 in the place of x :
= ( 5 × 7 ) - 2 = 33
= 35 - 2 = 33
LHS = RHS
Therefore , the weight of of smaller bag of seed is 7 pounds .