p -> q is represented as "If you have a library card, then you can check out books"
~q -> ~p is represented as "If you cannot check out books, then you do not have a library card" This is contrapositive by definition.
q -> p is represented as "If you can check out books, then you have a library card" This is the converse
~p -> ~q is represented as "If you do not have library card, then you cannot check out books". This is the inverse
p <-> q is represented as "You have library card if and only if you can check out books". This is the biconditional.
Since we're looking for a whole number of pairs, we can round down x to the nearest whole number. Therefore, Warren rented 11 pairs of shoes. Warren rented 11 pairs of shoes.
To find the number of pairs of shoes rented, we need to use the information given about the payment and number of lanes rented. If Warren paid $23.85 and received no change, then we can assume that the total cost of renting the lanes is exactly $23.85. Let's divide this amount by the cost of renting one pair of shoes to find the number of pairs rented.
Let's say the cost of renting one pair of shoes is $x. Since Warren rented 2 lanes, the total cost of renting the lanes is 2 times the cost of renting one pair of shoes, which is 2x.
Therefore, we can set up the equation 2x = 23.85 and solve for x. Dividing both sides of the equation by 2, we get x = 11.925.
Since we're looking for a whole number of pairs, we can round down x to the nearest whole number. Therefore, Warren rented 11 pairs of shoes.
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