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Math Help - Set Intersection Ratio and Set Difference Inequality Proof

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    Set Intersection Ratio and Set Difference Inequality Proof

    The problem in question is Given that A1 and A2 are subsets of a universal Set and that
    Set Intersection Ratio and Set Difference Inequality Proof-one.png

    Prove also that

    Set Intersection Ratio and Set Difference Inequality Proof-one.png.

    I've tried a number of things, such as multiplying similar ratios and forms of the number one, however it always leaves me with an expression that doesn't simplify. I've also tried to use a number of the basic identities of union, intersection, set difference, and complements, but to no avail.

    I'm avoiding using the base formula of the principle of inclusion/exclusion, as it is not introduced until after this problem, however I'm not opposed to using it if it is necessary. I'm mostly looking for ideas for what I should try (as I have run out by now), rather than an overall solution, but I'd appreciate any input.

    Thank you.
    Attached Thumbnails Attached Thumbnails Set Intersection Ratio and Set Difference Inequality Proof-one.png   Set Intersection Ratio and Set Difference Inequality Proof-one.png  
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