In Cat on a Hot Tin Roof, Big Daddy's use of the word "mendacity" includes deceit through omission of the truth and partial truths, deception, and even subterfuge, all of which are present to some degree in each of the characters; in fact, mendacity propels the drama as so often there are no clear-cut truths or lies. 

• Brick and Margaret (Maggie)

The grief that he feels over the death of his close friend Skipper has caused Brick to sink deeper into his alcoholism as he waits for the "click" which will shut down his melancholic thoughts and growing antipathy for his wife because he believes in her involvement in Skipper's suicide. And, apparently Maggie has not been completely honest with Brick about what happened between her and Skipper. But, she eventually reveals to her husband her involvement with Skipper--only it differs from the half-truths that Brick has believed. For, when Brick was injured and could not play in one of their football games, Skipper became drunk and cost the team the game. Angry with him, Maggie told him as they drank together that night to stop loving her husband or tell Brick that he must let Skipper admit his feelings. Skipper slapped her; so, she went to his room that night and pretended that she wanted him. But, Skipper was unable to prove his manhood, so, as Maggie tells her husband, she crashed through his mendacity:

--In this way, I destroyed him, by telling him truth that he and his world which he was born and raised in, yours and his world, had told him could not be told?

By telling Brick this truth, Maggie has broken through Brick's self-deception as well, and his broken ankle and hobbling with a crutch symbolize this weakening.

• Big Daddy and his family

In Act II, the huge console that contains a television, radio, and liquor cabinet fills a room downstairs acts as a symbol of this overriding mendacity. When asked by Mae to turn on some music, Brick finds a Wagnerian opera knowing that she is too crass and uncultured to appreciate such music, but Big Daddy shouts for it to be shut off. As Williams notes in the stage directions, this console serves as a shrine to the "comforts and illusions" of the characters because they turn to it for distraction from the conflicts. While the family gathers, the Reverend Tooker, whom, according to stage notes, is "the living embodiment of the pious conventional lie," hints at stained glass windows for his church as he anticipates the death of Big Daddy; however, the patriarch hears his innuendos and puts an end to them. At another point in the play, a lull in other conversations allows the Reverend to be overheard as he crassly jokes to Dr. Baugh about the Stork and the Reaper "running neck to neck" at the Pollitt home.

Having been deceived by Dr. Baugh, Big Mama has  informed Maggie and Brick that her husband only has a spastic colon; she, then, acts in a ribald manner, catching the minister in her lap after he tries to get up. She laughs raucously; Gooper and Mae cringe as they have been trying to rise in social circles and Big Mama's behavior is something they wish to conceal and deceive people about.

Further in this scene, Big Daddy accuses Big Mama of trying to take over the family in anticipation of his death; this cruel remark hurts Big Mama, who genuinely loves her husband and believes he is not going to die.

BIG DADDY
Ain't that so, Ida? Didn't you have an idea I was dying of cancer and now you could take control of this place and everything on it?

Then, Big Daddy calls their marriage a hypocrisy. Mama leaves, broken, telling her husband that she has always loved him. Alone, he merely remarks,"wouldn't it be funny if that was true…." because has heard so many untruths that he cannot believe what is true.

He then takes Brick privately aside and talks to him at length, revealing that he would like to leave everything to Brick, but cannot if he does not stop drinking. Brick and Big Daddy finally become honest with one another after many conversations filled with mendacity. Big Daddy tells Brick after learning of the relationship he and Skipper have had that they have discovered the lie at the center of the disgust which drives Brick to drink. And, Brick in retaliation, urges Big Daddy to consider the untruth behind the birthday wishes given him: He will have no more birthdays. Quickly, Brick tries to retract this revelation, but it is too late. However, he urges his father to be honest with him from now on and they can, then, be friends, putting away all the "mendacity."

In the final act, the others wonder where Big Daddy has gone; Big Mama assumes he has gone to bed. Soon, the family members begin haggling, and the conflict between Gooper and Mae with Maggie becomes vituperative as they seek to reveal the truths about one another. Big Mama appeals to Brick, saying if he would only have an heir, Big Daddy would leave his estate to him. Ironically, it is the lie of Maggie that she is pregnant that resolves this conflict. When Gooper and Mae question her honesty, their mendacity lends them no credibility; therefore, Maggie is believed. So, that evening, she withholds her husband's liquor from him in order that they can "make the lie true." 

Tennesse Williams writes about the fatal power of lies and deceit, worms that eat away at the fabric of a family or a society as a whole. So often in order to maintain harmony, families, or even societies, will fabricate reality. But, the consequences of these softening of harsh realities ( lies and mendacity) are always more devastating than the initial truth would have been.