已知集合$A=\{1,2^a\},B=\{a,b\}$若$A\cap B=\left\{\frac{1}{2}\right\}$,则$A\cup B$为(    )

    Mrs Smith's living room is large. There is a television in the room. The television is near the window. There are some magazines on the television. There is a table in the room. There are some newspapers on the table. There are some armchairs in the room. The armchairs are near the table. There is a stereo in the room. The stereo is near the door. Mrs Smith often listens to music from it.