Which of these is a chemical change? paper is shredded. gas is burned. ice melts. metal foil is heated.

Anything that says burned is a chemical reaction or a chemical change. Here's a burning reaction.

C2H5OH + 302 ===>  2CO2 +  3H2O

This is the equation for burning alcohol (the kind you drink). When burned, the alcohol's reaction leaves a beautiful blue flame along with CO2 and H2O on the right side.

So B is the answer.

You're not doing anything to paper if you shred it except make it smaller. It retains all of its chemical properties and almost all its physical properties.

Ice melting doesn't do anything to the water when it changes phase except you now have a puddle on the table where the ice (cube) was.  But you are still dealing with water.

Metal foil is heated, again the foil is left with all its chemical properties in tact. You can reuse the foil if you are cooking potatoes  in an open fire. Nothing has altered the chemical properties of the foil.  

b.transmitters send radio waves, and receivers capture radio waves.