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On air, the weather man gave the audience a mug in the plaza. He asked her where she was from. Then she told him about her hometown and began to flatter him. She loved to watch him and, very funny to me, she had a young daughter. The weather man could not get rid her in a polite way. I was watching and laughing because it seemed kind of embarrass. The woman had no shame of herself. I didn’t believe she invited him to her home and mentioned that she had a young daughter. It looked as if she was not attractive enough but her daughter was.

Are they correct?

Thank you
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The highlighted parts do not make sense. A mug? That's a type of cup. The final sentence - attractive enough for what?

On air, the weather man gave the audience a mug in the plaza. He asked her (who?) where she was from. Then she told him about her hometown and began to flatter him. She loved to watch him and, very funny to me, she had a young daughter. The weather man could not get rid of her in a polite way. I was watching and laughing because it seemed kind of embarrassing. The woman had no shame. I couldn't believe she invited him to her home and mentioned that she had a young daughter. It looked as if she was not attractive enough but her daughter was.
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Nona The BritThe highlighted parts do not make sense. A mug? That's a type of cup. The final sentence - attractive enough for what?

In AE 'mug' is used for 'face' (often not complimentary). A 'mug shot' is the photo of a person who has been arrested.
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Oh yes, mug-shot. Emotion: smile I couldn't work out why a weather man was giving his audiences mugs!

Anyway, mug-shot is not really appropriate herre either. Very informal and, as Philip says, often not very pleasant.
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< She loved to watch him and, very funny to me, she had a young daughter. >

"Mug" is fine there. What was funny about her having a young daughter? We need to know.

>I was watching and laughing because it seemed kind of embarrassing.

Probably better, "I was laughing while watching, because it seemed kind of embarrassing."

>"The woman had no shame." (Omit the reflexive.)

>I didn’t believe it when she invited him to her home and mentioned that she had a young daughter.

>It looked as if she was not attractive enough but her daughter was.

She was not attractive enough to whom?
Mug, even in the sense of face, is NOT ok there.