試題分析:(1)通過問題的等價(jià)轉(zhuǎn)化,然后解一個(gè)簡單的指、對(duì)數(shù)不等式即得答案,但是有一個(gè)易錯(cuò)之處:“
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”這里錯(cuò)在不是等價(jià)轉(zhuǎn)化,切記去掉對(duì)數(shù)符號(hào)后一定要保證真數(shù)為正;(2)解決此問題,對(duì)邏輯分析問題的能力要求比較高,首先要掌握邏輯用語的知識(shí),然后還需借助集合的語言來描述,最終回到不等式求解,且需關(guān)注細(xì)節(jié):端點(diǎn)是否帶等號(hào),這樣才能善始善終.
試題解析:(1)命題“
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”是假命題,則
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, 2分
即
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,
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,解得
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5分
(2)因?yàn)?img src="http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824060408285443.png" style="vertical-align:middle;" />是真命題,則
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和
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都為真命題. 6分
法一:因?yàn)?img src="http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824060408083313.png" style="vertical-align:middle;" />是真命題,則
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的解集的補(bǔ)集是
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解集的子集;
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是真命題,則
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的解集與
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的交集非空.
①若
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,則
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.
又∵
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,
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或
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,
∴
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是
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的解集的子集.
又由
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(其中
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),解得得
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或
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,
因此
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. 9分
②∵當(dāng)
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時(shí),
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,
∴問題轉(zhuǎn)化為
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,使得
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,
即
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的解集與
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的交集非空.
即
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,則
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, 13分
綜合①②可知滿足條件的
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的取值范圍是
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14分
法二:當(dāng)
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時(shí),
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,因?yàn)?img src="http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824060408083313.png" style="vertical-align:middle;" />是真命題,則
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,
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,即
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9分
當(dāng)
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時(shí),
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,因?yàn)?img src="http://thumb.zyjl.cn/pic2/upload/papers/20140824/20140824060408192310.png" style="vertical-align:middle;" />是真命題,則
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,使
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,
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,即
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13分
綜上所述,
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. 14分