Oscar Wilde treats truth in a trivial, unimportant manner in Act I of The Importance of Being Earnest.
Many of the characters introduced in Act I lie about both minor and major things.
At the beginning of the Act, Algernon orders the servant, Lane, to make cucumber sandwiches for his Aunt Augusta who will soon be visiting. Algernon insists these sandwiches are her favorite, which is why it is so important that they are ready by the time she arrives. However, by the time she does arrive, Algernon has eaten all the sandwiches himself. Instead of telling the truth about the sandwiches, Algernon plays ignorant and even puts the spotlight on Lane, asking him why there are no cucumber sandwiches even after he made sure to order them specially for Aunt Augusta's visit. This leads to yet another lie. Lane, although he knows he made the sandwiches and served them earlier to Algernon on a platter, dishonestly claims that there were no cucumbers at the market that morning. The interaction takes place like this:
ALGERNON: [picking up empty plate in horror]. Good heavens! Lane! Why are there no cucumber sandwiches? I ordered them specially.
LANE: [gravely]. There were no cucumbers in the market this morning, sir. I went down twice.
ALGERNON: No cucumbers!
Even though both characters know very well there were cucumber sandwiches, they both lie in order to hide the fact from Aunt Augusta.
On a more serious note, both Algernon and Jack are dishonest to those around them when they want to be excused from their homes and other business they don't want to take care of. Because of this, they are both considered a "Bunburyist" as stated by Algernon. In his explanation, a Bunburyist is one who invents a fictitious person in order get out of town as often as they like. Algernon has created a person named Bunbury:
ALGERNON: I have invented an invaluable permanent invalid called Bunbury, in order that I may be able to go down into the country whenever I choose.
Algernon explains how he uses Bunbury to his advantage:
ALGERNON: If it wasn't for Bunbury's extraordinary bad health, for instance, I wouldn't be able to dine with you at Willis's tonight, for I have been really engaged to Aunt Augusta for more than a week.
Algernon proves this later in Act I when he pleads to Aunt Augusta that he must cancel their dining plans that evening because his poor friend Bunbury is very sick again.
Jack, similar to Algernon's Bunbury, creates a fictitious brother. He uses this brother, named Ernest, as an excuse to get out of the country because he has to aid this brother in getting out of his latest mischief.
Jack: I have always pretended to have a younger brother of the name of Ernest, who lives in the Albany, and gets into the most dreadful scrapes.
It is a double offense that both men not only fabricate people, but that they do so in order to lie to their family and friends and get out of their obligations to them.
Jack admits he is Jack in the country, while he is Ernest in town. Algernon is guilty of constructing a false relationship with an ill friend. Lane cedes to Algernon's lie by taking responsibility for missing sandwiches that he did in fact prepare. Wilde uses his characters to portray the idea of truth as an insignificant part of communication with others.