为什么点击按钮“女”，出现的内容依旧是“男性”？

Question

<input type="button" id="man"  value="男" onclick="show()" checked="checked" >

<input type="button" id="woman" value="女" onclick="show()" checked="checked">

<p style="display:none" id="div1">男性</p>

<p style="display:none" id="div2">女性</p>

</body>

<script type="text/javascript">

function show(){

if(document.getElementById("man").checked){

document.getElementById("div1").style.display="block";

document.getElementById("div2").style.display="none";

}

else if(document.getElementById("woman").checked){

document.getElementById("div2").style.display="block";

document.getElementById("div1").style.display="none";

}

}

</script>